Question

Clarification question:
Say you have the function: csc(x^2+ 1)^(3)

When you take the derivative of csc(x), you get: -csc(x)*cot(x).

csc is the outer function. When we take the derivative of this, is it going to end up like this for the function at the beginning:

f(x) = csc(x^2+ 1)^(3)
then
f'(x) = -csc(x^2+1)^3 * cot(x^2 + 1)^3 * d(x^2 + 1)^3)/dx

?
Do you distribute the inner function to both the -csc and cot that come out from taking the derivative of the outer fcn csc?

Answer 1

use power rule

-3(csc x^2+ 1)^2(csc x^2+ 1)(cot x^2+ 1)(2x)