1. ## Differentiation

Differentiate $x^{\sin x}$
I know this has got something to do with the formula $\frac{d}{dx}(a^x)=(a^x)(\ln a)$ but i don't know how to do it. I tried using the chain rule but couldn't even figure it out. I need some pointers on how to do it.
Thanks for any help

2. $x^{\sin(x)} = exp[\sin(x) \ln(x)]$

to differentiate it . Let $u = \sin(x) \ln(x)$

$D(e^u) = e^u D( u )$

and $D (u) = \ln(x) D(\sin(x)) + \sin(x) D (\ln(x))$

what's next?

3. so I have:
$\frac{d}{dx}(e^u)=e^u(\ln x\cos x+\frac{\sin x}{x})=e^{\sin x\ln x}(\ln x\cos x+\frac{\sin x}{x})$
But this is not the answer. I'm supposed to give $x^{\sin x}(\ln x\cos x+\frac{\sin x}{x})$ so i don't know how the $\ln x$ disappears.
Thanks

4. Oh! ok, I see it now. $e^{\ln x}=x$ Am I right?

5. Yep..