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 # using the product rule?