differentiate y=e^sin(arclogx)

Question

alfie · Answer

do you mean...?

$$y= e^{\arcsin(logx)} ?$$

anonymous · Answer

that arc actually means square root. and it is (arclogx)

alfie · Answer

So like this?

$$e^{\sin{\sqrt{logx}}}$$

anonymous · Answer

yep.

alfie · Answer

Okay then, there are several functions nested one into another, we have to use the chain rule, you know how to do that?

alfie · Answer

Let's start from the one which is more external, then step by step "go deeper". 

$$e^{\sin{\sqrt{logx}}} \rightarrow = e^{\sin{\sqrt{logx}}}$$

Now.

$$\sin{\sqrt{logx}} \rightarrow  = \cos{\sqrt{logx}}$$

Deeper!

$$\sqrt{logx} \rightarrow \frac{1}{2x \sqrt{logx}}$$

Merge everything and get...

$$\huge \frac{e^{\sin{\sqrt{logx}}} \cos{\sqrt{logx}}}{2x \sqrt{logx}}$$