Question

Is the derivative of y=2(x+1)^3 equal to (6X+2)^2

Answer 1

No.
\[\begin{align*}
\frac{\mathrm{d}}{\mathrm{d}x}\left[2(x+1)^3\right]&=2\frac{\mathrm{d}}{\mathrm{d}x}\left[(x+1)^3\right]&\color{lightgray}{\text{factor out constants}}\\[1ex]
&=2\times3(x+1)^2\frac{\mathrm{d}}{\mathrm{d}x}\left[x+1\right]&\color{lightgray}{\text{power/chain rule}}\\[1ex]
&=6(x+1)^2
\end{align*}\]which is not equal to \((6x+2)^2\). The only way to move the \(6\) in front into the squared term is to write
\[6(x+1)^2=\left(\sqrt6\right)^2(x+1)^2=\left(\sqrt6x+\sqrt6\right)^2\]

Answer 2

I've get it now. Thanks.

Answer 3

How's that again? Sqrt(6) is not part of the expression for the derivative.

Answer 4

"Is the derivative of y=2(x+1)^3 equal to (6X+2)^2:" You must first apply the Power Rule, and then apply the Chain Rule.