00:01
In this question, we are given the equation z equal to e to the x times side of the x plus y, sorry, it will be y plus z, and we'll need to find the d z over the d x, also d z over the d y.
00:22
Now let's try to find the d z over the d x first.
00:28
In this case, x is a variable, y will be the constant, z is a function on the x and here first we need to apply the product rule so we will have it will be also this one will be the dz over the dx it will equal to here the product rule says we have e power x times side on the y plus z and then we will have plus e to the x times derivative of the side which we can equal to the cosine y plus and by the general, we need to 5 times the derivative of the inside.
01:09
We'll be derivative of the y.
01:10
Why is a constant now, so we will be 0 plus derivative of the z.
01:15
We have the dz over the dx.
01:19
And from here we will bring this one which is equal to times this.
01:25
We will times this guy.
01:27
We're going to bring this one to the other side and factor the dz over the dx outside.
01:33
And we have one minus.
01:35
E to the x, cosine of the y plus z, and then equal to e spell x, then size of the y plus z...