Derivative with respect to x and y of e^(x*sin(y))

Also stuck on this question. Help please :C

I assume you are working with partial derivatives.

To get the derivative WRT x, take the derivative of the function treating y as a constant:

f(x) = e^(x sin(y))

f'(x) = e^(x sin(y)) d/dx (x sin(y))

......= e^(x sin(y)) (sin(y))

......= sin(y) e^(x sin(y))

To get the derivative WRT y, take the derivative and treat x as a constant:

f(y) = e^(x sin(y))

f'(y) = e^(x sin(y)) d/dy (x sin(y))

......= e^(x sin(y)) (x cos(y))

......= x cos(y) e^(x sin(y))