Hi all,

I'm learning the rules of differentiation, specifically the product rule. I understand the steps to obtain an answer, but am stuck when it comes to simplifying and taking out a common factor. For example, the answer to one of the problems is:

dy/dx = x^{2}[6(2x + 1)^{2}] + (2x + 1)^{3}(2x)

I understand how to obtain this answer, but not the simplification. Continuing.....take out a common factor 2x(2x + 1)^{2}.

Apparently, this goes into the first term 3x times. And the second term 2x + 1 times. Resulting in:

dy/dx = 2x(2x + 1)^{2}[3x + (2x + 1)]

dy/dx = 2x(2x + 1)^{2}(5x + 1)]

As always, thanks for any help. I'd appreciate if someone could show me, step by step.

B.

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