Question

Find the derivative of (Cosx/1+sinx)^5​

Answer 1

Use the Chain Rule:

`(d)/(dx) [f(g(x))] = f'(g(x)) * g'(x)`

Given Information:

`f(x) = x^5\\ g(x) = (cos(x))/(1) +sin(x)\\ f(g(x)) = ( (cos(x))/(1) +sin(x))^5\\ \\ f'(x)=5x^4\\ g'(x)=(-sin(x))/(1) + cos(x)\\f'(g(x))*g'(x)=5((cosx))/(1) + sin(x))^4*((-sin(x))/(1) + cos(x))`

The answer is:

`5((cosx))/(1) + sin(x))^4*((-sin(x))/(1) + cos(x))`