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

1 Answer
Mar 21, 2016

Answer:

#(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))#