How do you differentiate $((5x+1)^2)(2x-1)$ ?

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Answer 1 · 2015-03-30T13:51:43

Use the Product Rule and Chain Rule:

$f'(x)=(5x+1)^{2}\cdot 2+2(5x+1)\cdot 5\cdot (2x-1)$ .

This can be simplified in a couple ways. Probably the most useful way is to leave it in a factored form:

$f'(x)=2(5x+1)(5x+1+10x-5)=2(5x+1)(15x-4)$

That way, you can quickly see the critical points of $f(x)$ are $x=-\frac{1}{5}$ and $x=\frac{4}{15}$ .

How do you differentiate ((5x+1)^2)(2x-1)((5x+1)^2)(2x-1)?