Question

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

Answer 1

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

Explanation:

We have to use here the concept of function of a function which uses the formula of chain rule.

As `f(x)=sqrt(g(x))` where `g(x)=e^(h(x))` and `h(x)==-x^2+x` according to chain rule

`(df)/(dx)=(df)/(dg)xx(dg)/(dx)xx(dh)/(dx)`

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

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