differentiate e^xcosx?

Question

i know it involves cahin rule, but i can't quite figue it out

Answer 1

y = (e^x) (cos x)
dy/dx = (e^x) (cos x) - (sin x) (e^x)
dy/dx = (e^x)( cos x - sin x)

Answer 2

let u=xcos(x)
y=e^u
dy/dx=e^u(du/dx)
Use the product rule to find du/dx
d[f(x)g(x)]=f(x)g'(x)+g(x)f'(x)
du/dx=cos(x)-xsin(x)
dy/dx=e^(xcos(x)) [cos(x)-xsin(x)]