How do you differentiate f(x)=4x*(x+3)*cosx using the product rule?

1 Answer
Dec 12, 2015

f'(x)=8xcosx+12cosx-4x^2sinx-12sinx

Explanation:

According to the product rule:

f'(x)=(x+3)cosxd/dx[4x]+4xcosxd/dx[x+3]+4x(x+3)d/dx[cosx]

Find each derivative:

d/dx[4x]=4

d/dx[x+3]=1

d/dx[cosx]=-sinx

Plug them back in.

f'(x)=4(x+3)cosx+(1)4xcosx+4x(x+3)(-sinx)

f'(x)=8xcosx+12cosx-4x^2sinx-12sinx