1 00:00:00,390 --> 00:00:07,380 In this letter I will describe that how to find the chief returns and how to find that integration of 2 00:00:07,380 --> 00:00:09,480 our function. 3 00:00:09,540 --> 00:00:11,000 So let me start. 4 00:00:11,080 --> 00:00:20,160 How to find the derivatives and what are the following that on Main used for derivatives and integrations 5 00:00:20,280 --> 00:00:21,470 in Matlab. 6 00:00:22,260 --> 00:00:28,560 So you will just type seems OK right over here. 7 00:00:28,650 --> 00:00:31,200 Sims and 8 00:00:35,450 --> 00:00:49,640 Sims X then you write the function just like clean writing or here f is equal to in line and inside 9 00:00:49,640 --> 00:00:52,490 the parenthesis so you will write the function. 10 00:00:54,250 --> 00:00:55,650 Okay. 11 00:00:56,870 --> 00:01:09,500 Yes you will go to the function that I am writing the function or here it is X X clear X squared plus 12 00:01:09,580 --> 00:01:19,670 1 Okay inside a double quotation mark then you will write the comma and after writing the comma inside 13 00:01:19,700 --> 00:01:24,150 the double quotation marks you will write x. 14 00:01:24,320 --> 00:01:33,350 So this means that you are going to finding the true written with respect to X.. 15 00:01:33,560 --> 00:01:34,380 Okay. 16 00:01:34,990 --> 00:01:36,000 Yes. 17 00:01:36,200 --> 00:01:45,230 No it will be equal to this function and to know will you will just type differentiation. 18 00:01:45,290 --> 00:01:58,850 D I would love inside the pen since you will write f of x f of x or more X yes and then you'll press 19 00:01:58,850 --> 00:01:59,560 the internal button. 20 00:02:00,200 --> 00:02:08,990 So this is that she wrote a love X plus one note will take another function just like before taking 21 00:02:08,990 --> 00:02:09,800 on the functions. 22 00:02:09,830 --> 00:02:13,510 I will first cleared it clear command window. 23 00:02:14,270 --> 00:02:24,970 Okay again you will write Sims X seems X and not here. 24 00:02:26,240 --> 00:02:39,390 Yes G is equal to I am taking with here G is equal to in line G is equal to an inside the parenthesis 25 00:02:39,450 --> 00:02:48,200 you and uh insert the parenthesis and inside the double quotation mark will right over here. 26 00:02:48,470 --> 00:02:57,650 Sign of X yes sign off X and do it by. 27 00:02:57,950 --> 00:03:03,170 It is because of X cause of X 28 00:03:06,660 --> 00:03:14,820 and yes since we have to write it inside the double quotation mark. 29 00:03:14,880 --> 00:03:23,130 And here you write that insert the comma and since we are going to fly in the derivative with respect 30 00:03:23,370 --> 00:03:33,620 to no real insert the double quotation marks and then you will grade X. So G is equal to. 31 00:03:33,690 --> 00:03:42,010 Okay so that is equal to this function sine of X do it because of X.. 32 00:03:42,040 --> 00:03:48,870 Okay here you can take that just like G N to 0. 33 00:03:49,130 --> 00:03:53,230 Yes the interval 0 is equal to zero. 34 00:03:53,520 --> 00:04:00,360 So this means that the function is defined because when the value of a function exist then that means 35 00:04:00,360 --> 00:04:03,830 that there are two you can find that add to it. 36 00:04:03,860 --> 00:04:07,720 So trivial can be found only for a finite function. 37 00:04:08,890 --> 00:04:12,130 Okay so this means that we can find that limit. 38 00:04:12,630 --> 00:04:23,820 So differentiation of T affects G of X with respect to X.. 39 00:04:24,690 --> 00:04:32,260 Okay so the definition differentiation on deal X with respect to X it will be equal to. 40 00:04:32,620 --> 00:04:34,040 Yes. 41 00:04:34,110 --> 00:04:43,790 This is you can avoid the pretense at the party and say that yes pretty arms and insert the Britain. 42 00:04:44,430 --> 00:04:47,160 So this is actually the answer. 43 00:04:47,360 --> 00:04:51,750 Same skill X due about two plus one. 44 00:04:52,730 --> 00:04:53,560 Okay. 45 00:04:53,940 --> 00:05:01,020 Science X development cost X not let us do spirit X extra by cost could x last one. 46 00:05:01,340 --> 00:05:03,490 Okay now we take. 47 00:05:04,530 --> 00:05:11,920 So there are a lot of courts to find that true bit of Matlab course to find the tutors. 48 00:05:12,010 --> 00:05:27,420 Here I am taking without wasting any time since x is equal to F is equal to three yes three multiplied 49 00:05:27,450 --> 00:05:46,840 by three multiplied by exponential exponential of X plus sign of X plus sine of x and yes minus five 50 00:05:46,840 --> 00:05:50,110 who would X clear minus. 51 00:05:50,740 --> 00:05:56,970 Yes it is five divided by X and skill. 52 00:05:57,210 --> 00:06:04,230 Okay this and uh now we're fine we want to find the transition. 53 00:06:04,730 --> 00:06:15,670 Uh yes this is a function differentiation of o f Okay so the defense transition of F is. 54 00:06:16,060 --> 00:06:18,040 So this is a good answer. 55 00:06:18,940 --> 00:06:26,790 And if we want to see the pretty answer then you will tie this to like s answer. 56 00:06:28,420 --> 00:06:38,290 So this is the pretty answer we call the x plus three it is to the x plus then do it by X Cube is the 57 00:06:38,290 --> 00:06:38,830 answer. 58 00:06:39,710 --> 00:06:40,380 Okay. 59 00:06:40,480 --> 00:06:47,860 No it isn't the pink that if we want to find the double G 12 since this is a single derivative. 60 00:06:48,430 --> 00:06:57,370 And if we want to find that trigger to then uh yes f commando means that we want to find the topology. 61 00:06:57,550 --> 00:07:04,030 And so this is that ambiguity in this was the director of causes sine minus sign. 62 00:07:04,030 --> 00:07:05,460 So this is the. 63 00:07:06,640 --> 00:07:06,880 Okay. 64 00:07:06,880 --> 00:07:15,420 And similarly if you want to find the third derivative third T riddles of this function f come on three. 65 00:07:16,000 --> 00:07:24,260 Okay then the third tree with two of this function is this. 66 00:07:24,410 --> 00:07:25,180 Okay. 67 00:07:25,280 --> 00:07:31,510 And suppose that uh easy plot. 68 00:07:31,550 --> 00:07:35,910 We want to these C plot of. 69 00:07:36,140 --> 00:07:50,210 Well uh suppose if I want to control let's see and you go to the control plus V easy plot okay. 70 00:07:50,340 --> 00:07:56,640 A C plot yes this is 71 00:07:59,790 --> 00:08:05,660 okay we will insert the same function over here and or under section. 72 00:08:06,120 --> 00:08:11,560 When we have one this easy plot off for this then it'll find. 73 00:08:11,730 --> 00:08:24,570 Yes this is the graph okay uh in the last uh functions that we find of sort of secondary event territory. 74 00:08:25,170 --> 00:08:25,720 Okay. 75 00:08:25,930 --> 00:08:30,690 No we check the those uh things just like uh. 76 00:08:30,770 --> 00:08:36,470 Uh first of all cleared it and was cleared out foot. 77 00:08:36,820 --> 00:08:38,260 And here a little. 78 00:08:38,310 --> 00:08:44,840 Again uh if we want to work in display command window. 79 00:08:45,130 --> 00:08:47,960 Okay so this is a command window. 80 00:08:47,970 --> 00:08:52,900 Uh yes I would like to work in command window. 81 00:08:53,450 --> 00:09:09,210 Sims and so we hear about Sims and Sims X and we will do the functions f you and fun is equal to execute. 82 00:09:09,870 --> 00:09:22,570 It is X cube last for x plus four and it is four x plus eight plus eight. 83 00:09:23,250 --> 00:09:25,950 And this function is a portal. 84 00:09:26,250 --> 00:09:37,830 And no we want to find out the front section of this function f of x 1 f n one comma X.. 85 00:09:38,160 --> 00:09:42,480 Okay then this is the derivative. 86 00:09:43,090 --> 00:09:43,460 Okay. 87 00:09:43,480 --> 00:09:56,260 And if we want to print that integration integration of this function 0 1 and 2 comma X complex and 88 00:09:56,680 --> 00:10:06,550 comma 2 comma 3 the limits are from 2 to 3 for the definite intent on you know integration of this function 89 00:10:07,970 --> 00:10:10,750 and gays are definitely integral from total total. 90 00:10:10,810 --> 00:10:13,630 It will be equal to. 91 00:10:13,900 --> 00:10:16,420 This is your answer 137 or 4. 92 00:10:17,770 --> 00:10:18,600 Okay. 93 00:10:18,650 --> 00:10:28,040 And I would change the function just like I am taking over here one is equal to. 94 00:10:28,310 --> 00:10:42,850 Here it is just like a complete complicated functions they might cause cause uh and to cause just like 95 00:10:44,460 --> 00:10:58,280 guess cost too much to fly by X and plus three plus sign in two three. 96 00:10:58,310 --> 00:11:06,150 Call my x 3 and uh and multiply by x. 97 00:11:06,150 --> 00:11:20,220 Okay so this is equal to uh cause 2 x Yes Los Angeles X and Y NC isn't all this function. 98 00:11:20,350 --> 00:11:21,080 Yeah. 99 00:11:21,230 --> 00:11:34,520 Function with respect to x and it will be equal to yes 3 sine prequels 3x minus 2 sine do X okay. 100 00:11:34,730 --> 00:11:49,070 And suppose if you want to find the integration integration of this function and to do over 3 to 4 or 101 00:11:49,660 --> 00:11:53,790 so on some will be equal just like s. 102 00:11:53,980 --> 00:12:00,710 And if we want to check the 40 answer then it is just like. 103 00:12:01,690 --> 00:12:03,190 So this is your pretty answer. 104 00:12:07,850 --> 00:12:09,050 And no 105 00:12:12,020 --> 00:12:13,360 I would like to. 106 00:12:14,330 --> 00:12:17,450 This is the GMAT. 107 00:12:18,110 --> 00:12:25,890 Okay and control plus C. 108 00:12:26,430 --> 00:12:32,800 Well if you want to check it it's a graph of the left move to the middle. 109 00:12:33,760 --> 00:12:34,590 Yes. 110 00:12:34,750 --> 00:12:35,540 Here you are right. 111 00:12:35,560 --> 00:12:39,930 Easy plot easy plot. 112 00:12:40,150 --> 00:12:40,810 Okay. 113 00:12:41,020 --> 00:12:45,220 And uh inside the easy blocked you on the right. 114 00:12:46,120 --> 00:12:47,640 Uh yes. 115 00:12:47,650 --> 00:12:50,500 Easy plot parenthesis 116 00:12:58,230 --> 00:12:58,670 okay. 117 00:12:58,690 --> 00:12:59,150 No. 118 00:12:59,200 --> 00:13:05,100 You could have run this section and so what kind of graph you will get over here. 119 00:13:06,250 --> 00:13:06,840 Yes. 120 00:13:06,850 --> 00:13:07,800 This is your graph. 121 00:13:07,810 --> 00:13:13,370 I'll take all three X and letters to sign 2 x. 122 00:13:13,980 --> 00:13:19,120 So again working towards the command window. 123 00:13:20,460 --> 00:13:23,870 Yes this is your command. 124 00:13:31,810 --> 00:13:36,350 I'll go and I will clear it on here. 125 00:13:43,290 --> 00:13:47,480 Yes we can also read it a little bit. 126 00:13:47,860 --> 00:13:50,160 I hear you a lot so. 127 00:13:50,790 --> 00:13:52,920 Yes. 128 00:13:52,920 --> 00:13:55,500 No we are taking it another. 129 00:13:55,500 --> 00:14:01,910 So there are many ways by which you can find the derivative in MATLAB matlab. 130 00:14:01,950 --> 00:14:06,530 So here we are writing Sims and x. 131 00:14:06,730 --> 00:14:18,620 No function is this like Y is equal to y is equal to 6 x 6 multiplied by. 132 00:14:19,290 --> 00:14:22,980 Yes it is just like multiplied by X. 133 00:14:23,030 --> 00:14:30,010 Uh yes let's say it does it. 134 00:14:30,090 --> 00:14:33,690 And uh anyway right. 135 00:14:33,710 --> 00:14:40,530 Easy plot the plot b c blotto. 136 00:14:41,640 --> 00:14:44,890 Yes or Y. 137 00:14:45,700 --> 00:14:55,620 And when you a ride easy plot on y you will get the. 138 00:14:55,670 --> 00:14:59,510 So this is your plotting which is a straight line. 139 00:14:59,540 --> 00:15:00,020 Yes. 140 00:15:00,050 --> 00:15:09,250 This is I'll get no again move towards the other window more here are you right. 141 00:15:09,480 --> 00:15:10,500 Punches. 142 00:15:11,360 --> 00:15:14,460 Oh for y. 143 00:15:14,530 --> 00:15:19,180 It will be equal to the transitional Y is equal to 6. 144 00:15:20,410 --> 00:15:22,540 Yes. 145 00:15:22,790 --> 00:15:23,030 No. 146 00:15:23,050 --> 00:15:27,230 Change the functional head clear this window no. 147 00:15:27,610 --> 00:15:35,410 Z is equal to Z is equal to same sex. 148 00:15:35,410 --> 00:15:42,130 Yes you will frustrate same sex and z is equal to 149 00:15:45,840 --> 00:15:46,950 working over here. 150 00:15:46,990 --> 00:15:51,460 X bar 3. 151 00:15:51,890 --> 00:15:52,520 Yes. 152 00:15:52,540 --> 00:15:53,420 2 multiply 153 00:15:58,110 --> 00:15:59,190 you little by it 154 00:16:04,020 --> 00:16:08,570 in order to avoid from any case of ambiguity 155 00:16:13,690 --> 00:16:17,480 divide also 3 inside up and this is okay. 156 00:16:17,500 --> 00:16:25,380 And then plus uh to execute working well here. 157 00:16:26,440 --> 00:16:30,400 Uh yes. 158 00:16:30,650 --> 00:16:32,490 That is true. 159 00:16:33,610 --> 00:16:38,590 And uh do it by uh do it by X cube 160 00:16:41,420 --> 00:16:45,930 it is X killed. 161 00:16:46,360 --> 00:16:51,720 Okay and to close this parenthesis. 162 00:16:51,850 --> 00:16:52,780 Okay. 163 00:16:53,070 --> 00:16:55,220 Uh no. 164 00:16:55,270 --> 00:16:57,600 It will be equal to this function. 165 00:16:57,790 --> 00:17:08,760 And if we take the easy plot easy plot of this function okay here's the plot of Z. 166 00:17:11,420 --> 00:17:14,600 Yes this will be equal to. 167 00:17:14,620 --> 00:17:16,280 We can check it in the 168 00:17:21,200 --> 00:17:21,890 this is. 169 00:17:24,770 --> 00:17:36,710 This is your output graph to execute and uh plus X Cuba with three. 170 00:17:37,480 --> 00:17:39,580 Again move to the window. 171 00:17:39,640 --> 00:17:50,200 He had to find the derivative differentiation of differentiation of y z. 172 00:17:50,250 --> 00:17:51,230 Here we're taking Z. 173 00:17:52,020 --> 00:17:55,760 So it will be equal to this hand. 174 00:17:55,880 --> 00:17:58,560 The integration and tuition. 175 00:17:58,580 --> 00:18:00,360 Arthur C.. 176 00:18:00,650 --> 00:18:05,480 Then it means that integration is this. 177 00:18:05,840 --> 00:18:16,710 And if we want to find a hand did wash it off easy and to want to show this will be close to 178 00:18:20,440 --> 00:18:20,950 okay. 179 00:18:21,020 --> 00:18:26,090 Now we check the record. 180 00:18:26,260 --> 00:18:27,440 Yes. 181 00:18:27,730 --> 00:18:32,650 Most likely in the command window and here will right. 182 00:18:32,650 --> 00:18:45,270 Since has since X and the function is Y is equal to inside the parenthesis and inside the parentheses 183 00:18:45,270 --> 00:19:00,170 you are right it is X all raised the bar skip class 3 x the last 3 x not 3 multiply by x okay. 184 00:19:00,260 --> 00:19:16,650 Two plus three to do what would be inside the parenthesis you will write X squared X say X skill minus 185 00:19:16,650 --> 00:19:23,650 three x minus 3 multiplied by X plus one plus one. 186 00:19:24,490 --> 00:19:28,030 So how do you get this function. 187 00:19:28,040 --> 00:19:28,730 Okay. 188 00:19:29,560 --> 00:19:32,670 Yes yes yes of course. 189 00:19:32,680 --> 00:19:39,600 And no we were contemplating the we want to find our differentiation. 190 00:19:39,770 --> 00:19:43,990 Of course this. 191 00:19:46,120 --> 00:19:46,620 Okay. 192 00:19:49,450 --> 00:19:50,930 It is. 193 00:19:51,290 --> 00:19:55,350 And if we John want to take the party on so 194 00:19:59,430 --> 00:20:02,530 property so 195 00:20:15,550 --> 00:20:21,540 nobody else is this guy okay. 196 00:20:21,550 --> 00:20:23,440 No. 197 00:20:23,440 --> 00:20:32,830 Suppose we want to uh differentiation. 198 00:20:34,330 --> 00:20:39,320 Differentiation all the way. 199 00:20:39,410 --> 00:20:44,360 And the second derivative will be equal to this. 200 00:20:44,650 --> 00:20:46,640 Okay. 201 00:20:46,830 --> 00:20:50,370 You want to check the body of this and the second to it. 202 00:20:50,650 --> 00:20:58,110 It is why this wouldn't be pretty on subsidy right. 203 00:20:58,140 --> 00:20:58,830 Pretty answer. 204 00:20:59,740 --> 00:21:00,300 Okay. 205 00:21:00,420 --> 00:21:02,720 This will be equal to this one. 206 00:21:03,090 --> 00:21:03,470 Okay. 207 00:21:05,400 --> 00:21:06,000 Yes. 208 00:21:08,140 --> 00:21:14,380 It static one is equal to execute minus three x plus one take. 209 00:21:15,340 --> 00:21:15,920 Okay. 210 00:21:16,020 --> 00:21:17,430 And skip. 211 00:21:18,490 --> 00:21:27,700 So what a beautiful you can do very tough calculations just in seconds in Matlab. 212 00:21:28,740 --> 00:21:29,930 Okay. 213 00:21:30,000 --> 00:21:30,430 No. 214 00:21:30,510 --> 00:21:48,260 Who we discuss and those functions just like uh we have same sex scenes X and we are going to yes say 215 00:21:51,420 --> 00:22:05,180 Sams X and uh here we are writing the transition means you can directly find that transition just like 216 00:22:05,180 --> 00:22:19,740 in writing fly multiply by x and despair Y if X skill and plus food x or x plus nine. 217 00:22:20,340 --> 00:22:32,700 Okay all right directly so it will be cool to yes what is simple and uh you can also write on is equal 218 00:22:32,700 --> 00:22:44,360 to one is a good do list like Y if X squared plus nine control plus C 219 00:22:49,140 --> 00:22:55,150 one is equal to this and here you are right. 220 00:22:55,230 --> 00:23:06,750 Once he is shown one section of the conversation one with respect to x. 221 00:23:07,540 --> 00:23:11,620 Okay this one we go to then it's possible again same. 222 00:23:12,040 --> 00:23:23,590 And it will want to find our differentiation off of this function of this function with respect to x 223 00:23:23,680 --> 00:23:33,990 x with respect X at X is equal to three then our answer will be this which is zero okay. 224 00:23:34,480 --> 00:23:39,220 Differentiation of this function then x plus 225 00:23:43,590 --> 00:23:46,930 of this one function at x is a. 226 00:23:47,140 --> 00:23:47,920 So 227 00:23:51,620 --> 00:23:54,800 no it is actually not indexed into it. 228 00:23:54,830 --> 00:23:57,050 This is not X is equal to three. 229 00:23:57,350 --> 00:23:58,910 It is actually targeting it. 230 00:23:59,300 --> 00:23:59,970 Okay. 231 00:24:00,050 --> 00:24:02,120 It is actually third derivative. 232 00:24:02,120 --> 00:24:02,800 Sorry. 233 00:24:03,080 --> 00:24:04,400 What does pollination. 234 00:24:04,690 --> 00:24:09,380 So differentiation inside the pants as you might find on my x commentary. 235 00:24:09,650 --> 00:24:11,740 Then this means that you are finding a third derivative. 236 00:24:11,840 --> 00:24:22,070 Okay so this is the V hole to find that integration and derivatives in MATLAB so all calculus is very 237 00:24:22,070 --> 00:24:32,420 easy o calculus is what is easy in MATLAB since in calculus we saw so many problems for many questions 238 00:24:32,930 --> 00:24:35,240 and they have very long calculations. 239 00:24:35,270 --> 00:24:38,540 But here you can solve it. 240 00:24:38,780 --> 00:24:40,760 Very simple calculations. 241 00:24:41,230 --> 00:24:48,680 Rather you have a very typical functions if you want to find a derivative of integration of all typical 242 00:24:48,680 --> 00:24:57,090 functions a little bit you can see abstract functions Matlab will solve your problem just 10 minutes 243 00:24:58,340 --> 00:25:04,070 and you can sketch about graphs you can plot the graphs off for derivative functions. 244 00:25:04,080 --> 00:25:10,360 Okay so this was the last time my course matlab. 245 00:25:10,360 --> 00:25:12,280 Hope you will enjoy this course. 246 00:25:12,530 --> 00:25:18,500 And if you have any kind of questions then you can ask me the questions in the class answer sections. 247 00:25:18,590 --> 00:25:22,310 I am here and I will give you the prompt response. 248 00:25:22,310 --> 00:25:27,120 It is not just like you will answer and you will work through this. 249 00:25:27,140 --> 00:25:33,310 No you will not be offered through this whenever you will for the answer for the question. 250 00:25:33,410 --> 00:25:41,790 I will give you the answer promptly so goodbye and wish you good luck for your future.