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