I am having trouble finding the local extremes for a particular function.

f(xy)=e^(2x)cosy

I have so far:

f'(x)= 2e^(2x)cosy

f'(y)=-e^(2x)cosy

f''(x)=4e^(2x)cosy

f''(y)=-e^(2x)cosy

f''(xy)=-2e^(2x)siny

Now I'm setting both f'(x) and f'(y) = 0, but this is where I'm having trouble. Does that mean that 2e^(2x)=0, cosy=0, -e^(2X)=0, and siny=0?

Thanks for any help that can be provided.