Question

How do you differentiate `f(x)=sqrt(1-e^(4x))` using the chain rule.?

Answer 1

`(df)/(dx)=(-2e^(4x))/sqrt(1-e^(4x))`

Explanation:

Here we use the concept of function of a function and use chain rule.

Here we have `f(x)=sqrt(g(x))`, where `g(x)=1-e^(h(x)` and `h(x)=4x`.

According to chain rule `(df)/(dx)=(df)/(dg)xx(dg)/(dh)xx(dh)/(dx)`

Hence `(df)/(dx)=1/(2sqrt(1-e^(4x)))xx(-e^(4x))xx4`

or `(df)/(dx)=(-2e^(4x))/sqrt(1-e^(4x))`