Question

derivate (2x)^x

Answer 1

\[\large (2x)^x=e^{\ln(2x)^x}=e^{x\ln2x}\]
Use the chain rule now:
\[\frac{d}{dx}[e^{x\ln2x}]=e^{x\ln2x}\frac{d}{dx}[x\ln2x]\]

Answer 2

so the answer is xln2x

Answer 3

No

Answer 4

\[(2x)^xln2x\]

is this right

Answer 5

Close, you're missing one term. Recall the product rule:
\[\frac{d}{dx}[x\ln2x]=\frac{d}{dx}[x]\ln2x+x\frac{d}{dx}[\ln2x]\]