What does ln2 equal? I'm stuck at that. Is there a formula for the derivative of ln(2^x)?

The problem is:

Use logarithmic differentiation to differentiate the following functions:

f(x)=2^x.

I got: ln(f(x))=ln(2^x)

d/dx [lnf(x)]=[f'(x)]/[f(x)=[x(2^(x-1)]/(2^x)

f'(x)=f(x)[x(2^(x-1)]/(2^x)=[x2^(x-1)]

But the answer says it's (2^x)ln2