Question

find all second partial derivatives of

f(xy)=xcosy+ye^x

Answer 1

$$f(x,y)=x\cos y+ye^x$$

$$f_x=\cos y+ye^x$$

$$f_y=-x\sin y+e^x$$

$$f_{xx}=ye^x$$

$$f_{xy}=-\sin y+e^x=f_{yx}$$

$$f_{yy}=-x\cos y$$