00:01
In this question, the equation given is z plus 9 equals to x into e to the power y cos z.
00:10
Now, let this is the function f with respect to x comma y comma z which is equals to z plus 9 minus x into e to the power y cos z and partial derivative of this function with respect to x.
00:31
So, that will be minus derivative of x is 1 into e to the power y cos z and partial derivative with respect to x.
00:42
So, here partial derivative of z with respect to x is 0 and 9 is also 0 because they are constant terms.
00:49
Now, partial derivative of f with respect to y.
00:53
So, again this term, this term will be 0.
00:55
So, this is equals to minus of x derivative of e to the power y is e to the power y into cos z and next partial derivative of f with respect to z.
01:10
So, partial derivative of z with respect to z is 1.
01:14
So, this will be 1 minus minus partial derivative of cos z.
01:21
So, that is keeping x and e to the power y as it is.
01:26
So, partial derivative of cos z is minus z with respect to z.
01:32
So, this is equals to 1 plus x e to the power y sin z.
01:40
Now, finding its value.
01:42
So, its value at 9 comma 0 comma 0.
01:48
So, this will be equals to minus of e to the power 0 and cos 0 because this represents x y z.
01:59
So, here value of x is 9, value of y is 0 and value of z is 0.
02:05
So, e to the power 0 anything raise to the power 0 is 1.
02:09
So, this will be minus 1 and cos 0 which is 1...