Question

what is the derivative of g(x)=(1-2x)^2(x-3)

Answer 1

looks like a product rule problem to me. plus some chain rule

Answer 2

\[g(x)=(1-2x)^2(x-3)\]
Use the product rule:
\[g'(x)=(1-2x)^2\frac{d(x-3)}{dx}+\frac{d((1-2x)^2)}{dx}(x-3)\]
Take the derivative where it says to, but don't forget about the chain rule:
\[g'(x)=(1-2x)^2(1)+2*2(1-2x)(x-3)\]
Clean it up a little...
\[g'(x)=(1-2x)^2+4(1-2x)(x-3)\]

Answer 3

Oh, shoot, I missed a negative sign when I did the chain rule. That should be a -2*2(...

Answer 4

\[g'(x)=(1-2x)^2-4(1-2x)(x-3)\]

Answer 5

why is it changing to - 4 i got \[+2(1-2x)^{-1}\],, is it wrong???

Answer 6

Did that 2 come from the exponent or from the chain rule?

Answer 7

exponent

Answer 8

Ah, okay. So you need to use the chain rule:
\[\frac{d((1-2x)^2)}{dx}=2(1-2x)^1\frac{d(1-2x)}{dx}\]
\[=2(1-2x)^1(-2)=-4(1-2x)\]