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

1 Answer
Shwetank Mauria
May 9, 2016

#(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))#

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