Question

Derivative of csc(e^x+1)

Answer 1

Do you know the derivative of \(\large \csc x\)?

Answer 2

-cscxcotx

Answer 3

Ok good. So applying that derivative here gives us,\[\large \left[\csc(e^x+1)\right]'\qquad=\qquad -\csc(e^x+1)\cot(e^x+1)\]But we also have to remember to apply the chain rule, multiplying by the derivative of the inner function that we started with. In this case, our inner function is the contents inside of the cosecant operation.\[\large \left[\csc(e^x+1)\right]'\qquad=\qquad -\csc(e^x+1)\cot(e^x+1)\color{royalblue}{(e^x+1)'}\]The prime is to show that we still need to take the derivative of that part.