Question

Question #4e3be

Answer 1

When you compute the partial derivative with respect to a variable, you treat all other factors and terms as though they are constants.

To compute the partial derivative of w with respect to x you treat `cos(y)` as though it was a constant and you compute the derivative of `e^x`:

`(delw)/(delx) = cos(y)(d(e^x))/dx`

This is a bad example because `(d(e^x))/dx = e^x` but this is the problem that we have:

`(delw)/(delx) = cos(y)e^x`

To compute the partial derivative with respect to y, you treat `e^x` as though it was a constant and compute the derivative of `cos(y)`:

`(delw)/(dely) = (d(cos(y)))/dye^x`

`(delw)/(dely) = -sin(y)e^x`