Find the derivative?

Question

How do you find the derivative of y=e^x cosx?

Answer 1

Derivative of e^x=e^x

Derivative of cosx=-sinx

Product rule:

y=f(x)g(x)

y'=f'(x)g(x)+f(x)g'(x)

y'=e^x(cosx)-e^x(sinx)

Answer 2

Property:

y=f(x)g(x)

y'=f'(x)g(x)+f(x)g'(x)

Solution:

y=(e^x)'cosx+e^x(cosx)'

y=e^x cosx+e^x(-sinx)

y=e^x (cosx-sinx)

Answer 3

y = e^xcosx

dy/dx = d/dxe^xcosx

         = e^xcosx (xd/dxcosx + cosxd/dxx)

         = e^xcosx (x(-sinx) + cosx(1))

         = e^xcosx (-xsinx + cosx)

dy/dx = (-xsinx + cosx)e^xcosx

This is your answer

Answer 4

y' = e^x -sinx