Question

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

Answer 1

`f'(x)==e^cot(1/sqrtx)xx-csc^2(1/sqrtx)xx(-1/(2x^(3/2)))`

Explanation:

`f(x)=e^x, g(x)=cotx, h(x)=1/sqrtx`

`f(g(h(x)))=e^cot(1/sqrtx)`

`[f(g(h(x)))]'=f'(g(h(x))xxg'(h(x))xxh'(x)`

`=e^cot(1/sqrtx)xx-csc^2(1/sqrtx)xx(-1/(2x^(3/2)))`