00:01
Hi, in this question, we have to govern that p equals square root of u square plus v square plus w square and u equals x e power y, v equals y e power x and w equals e power xy.
00:20
We need to calculate dou p by dou x and dou p by dou y when x equals 0 and y equals 3.
00:30
We have to use the chain rule to find the derivative.
00:35
So here, dou p by dou x equals dou p by dou u into dou u by dou x plus dou p by dou v into dou v by dou x plus dou p by dou w into dou w by dou x.
00:56
Similarly, dou p by dou y can be found by using the formula dou p by dou u into dou u by dou y plus dou p by dou v into dou v by dou y plus dou p by dou w into dou w by dou y.
01:19
So, first we have to calculate dou p by dou u which is equal to, on differentiating this we get 1 by square root of u square plus v square plus w square into 2.
01:42
On differentiating with respect to u, then we get 2u.
01:50
So which is equal to u divided by square root of u square plus v square plus w square.
01:57
Next we have to differentiate with respect to v.
02:00
So we get dou p by dou v equals 1 by 2 square root of u square plus v square plus w square into on differentiating with respect to v, then we get 2v.
02:17
So which is equal to v divided by square root of u square plus v square plus w square.
02:23
By similar way, dou p by dou w which is equal to w divided by square root of u square plus v square plus w square.
02:37
Next we have to calculate dou u by dou x which is equal to dou by dou x of x e power y.
02:47
Here e power y is constant.
02:49
So on differentiating x with respect to x, then we get 1 which is equal to e power y.
02:57
Next we have to calculate dou u by dou y which is equal to dou by dou y of x e power y.
03:04
Here we have to consider x as constant...