Question

How to find the derivative of:

y= x+ 2xln(2x)

Answer 1

\(\large y= x+ 2xln(2x)\implies
\begin{array}{llll}
y'=\frac{d}{dx}[&x]+\frac{d}{dx}[&2xln(2x)]\\
&\uparrow &\quad \uparrow \\
&\textit{power rule}&\textit{product rule}
\end{array}\)

Answer 2

Thank you!

Answer 3

Okay, so I'm confused on the product rule part. Can someone break it down for me?

Answer 4

The derivative of 2x times ln(2x) + derivative of ln(2x) times 2x

Answer 5

So that's be 2ln(2x)+ 1/x, right?

Answer 6

\[2x((1/2x)(2)) + \ln(2x)(2)= 2(\ln(2x)+1)\]

Answer 7

Thanks!