Question

How do you differentiate `f(x)=(cot(x))^2` using the chain rule?

Answer 1

`f'(x)=-2cot(x)csc^2(x)`

Explanation:

Use the chain rule. The first issue here is the second power. According to the chain rule, `d/dx[u^2]=2u*u'`, and here we have `u=cot(x)`, giving us

`f'(x)=2cot(x)*d/dx[cot(x)]`

The derivative of `cot(x)` is `-csc^2(x)`.

`f'(x)=-2cot(x)csc^2(x)`