Question

what is the derivative of csc(sqrt(x))

Answer 1

hey haynay :)

Do you recall the derivative of \(\Large\rm \csc(x)\) ?

Answer 2

-csc(x)cot(x)

Answer 3

Mmm k good good good.

Answer 4

\[\Large\rm \color{royalblue}{\left(\csc\sqrt{x}\right)'}=(-\csc\sqrt x~\cot\sqrt x)\cdot \color{royalblue}{\left(\sqrt{x}\right)'}\]Then you just have to chain rule after that.

Answer 5

Multiply by the derivative of the inner function (sqrtx in this case).

Answer 6

So that blue part still need to be differentiated.
Remember how to deal with sqrt x?

Answer 7

yes