Question

differentiate y=e^sin(arclogx)

Answer 1

do you mean...?

\[y= e^{\arcsin(logx)} ?\]

Answer 2

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

Answer 3

So like this?

\[e^{\sin{\sqrt{logx}}}\]

Answer 4

yep.

Answer 5

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

Answer 6

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...

\[\huge \frac{e^{\sin{\sqrt{logx}}} \cos{\sqrt{logx}}}{2x \sqrt{logx}}\]