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

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Answer 1 · 2015-12-12T14:08:46

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

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.

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

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

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