MHB Deriving f(x)=2x^x - Math Problem Solving

[bguillenwork]

So I have to derive f(x)=2x^x

I know I first set i equal to y

y = 2x^x

then take the natural log

lny = ln(2x^x)
lny = 2(ln2x)

but here I get a bit stuck. Do I take the derivative now?

 

[Prove It]

So I have to derive f(x)=2x^x

I know I first set i equal to y

y = 2x^x

then take the natural log

lny = ln(2x^x)
lny = 2(ln2x)

but here I get a bit stuck. Do I take the derivative now?

You need to review your logarithm laws...

$\displaystyle \begin{align*} \ln{(y)} &= \ln{ \left( 2 \cdot x^x \right) } \\ \ln{(y)} &= \ln{(2)} + \ln{ \left( x^x \right) } \\ \ln{(y)} &= \ln{(2)} + x\ln{(x)} \end{align*}$

and then yes, you will now differentiate both sides.