How do you differentiate $f(x)=(x^2+4x)(x+2)^2$ using the product rule?

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Answer 1 · 2017-10-29T22:18:09

Please see below.

$f'(x) = (2x+4)(x+2)^2+(x^2+4x)[2(x+2)]$

$= 2(x+2)(x+2)^2+2x(x+2)(x-4)$

$= 2(x+2)[x+2)^2+x(x-4)]$

$= 2(x+2)[x^2+4x+4+x^2-4x]$

$= 2(x+2)[2x^2+4]$

$= 4(x+2)(x^2+2)$

How do you differentiate f(x)=(x^2+4x)(x+2)^2f(x)=(x^2+4x)(x+2)^2 using the product rule?