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Answer 1 · 2018-01-05T03:27:35

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 $cos(y)$ :

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

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