Question

How do you differentiate `f(x)=cos(e^(x^4))` using the chain rule?

Answer 1

`(df)/(dx)=-4x^3e^(x^4)sin(e^(x^4))`

Explanation:

Here `f(x)=cos(g(x))`, where `g(x)=e^(h(x))` and `h(x)=x^4`

Hence, using chain rule

`(df)/(dx)=-sin(e^(x^4))xxe^(x^4)xx4x^3`

or `(df)/(dx)=-4x^3e^(x^4)sin(e^(x^4))`