Just confused on how to work this out. If you could show, I'd appreciate it
f(x)=x^sin(x)
I'm kicking myself rightnow for not seeing how to do it right.
from the title of your post i suppose you want to do this using logarithmic differentiation
in that case, i'll start you off
Let $\displaystyle y = x^{\sin x}$
$\displaystyle \Rightarrow \ln y = \ln x^{\sin x}$
$\displaystyle \Rightarrow \ln y = \sin x \ln x$
now differentiate implicitly. note you will need the product rule for the right hand side
can you continue?