Question

How do you differentiate `f(x)=cot(e^sqrt(x^2-1))` using the chain rule?

Answer 1

`d/dx f(x)=-csc^2(e^sqrt(x^2-1))(e^sqrt(x^2-1))(1/2(x^2-1)^-(1/2))(2x)`

Explanation:

`d/dxcot(x)=-csc^2(x)`
`d/dxe^x=e^x`
`d/dxx^n=nx^(n-1)`

`f(x)=cot(e^sqrt(x^2-1))`
`d/dx f(x)=-csc^2(e^sqrt(x^2-1))(e^sqrt(x^2-1))(1/2(x^2-1)^-(1/2))(2x)`