What is the derivative of this function?f(x)= (2x+1)^3(3x-x^2)

Asked on by utilityfan

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nathanshields | High School Teacher | (Level 1) Associate Educator

Posted on


Break it in the middle for a product rule:
d(first)*second + d(second)*first

To find derivative of the first piece, `(2x+1)^3` , we use chain rule:
d(inside)*d(outside with inside the same)


Derivative of the second piece, `3x-x^2` , is just `3-2x` .

Put it all together:
d(first)*second + d(second)*first =
`6(2x+1)^2*(3x-x^2)` + `(3-2x)*(2x+1)^3`

Maybe you could factor the (2x+1)^2 out:


That big second factor is only 2nd-order, so let's simplify that bad boy:



For even better looks, factor a -1 out of that second factor:


Cha-ching! Let me know what you think.

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