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

1 Answer
Bill K.
Mar 30, 2015

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}#.

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