Question

find derivative of x/sin raise to powern.x

Answer 1

I'm assuming you mean the question is:

$\frac{d}{dx}\left(\dfrac{x}{\sin\left(x\right)}\right)^x$

Here's your answer:

$\left(\dfrac{x}{\sin\left(x\right)}\right)^x\left(\ln\left(\dfrac{x}{\sin\left(x\right)}\right)+\dfrac{\sin\left(x\right)-x\cos\left(x\right)}{\sin\left(x\right)}\right)$

Simplifying:

$\dfrac{\left(\frac{x}{\sin\left(x\right)}\right)^x\left(\sin\left(x\right)\ln\left(\frac{x}{\sin\left(x\right)}\right)+\sin\left(x\right)-x\cos\left(x\right)\right)}{\sin\left(x\right)}$

And here's the steps: