How do you differentiate #f(x)=1/sqrt(1-x)# using the chain rule?

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Answer 1 · 2018-04-11T17:07:00

#f'(x)=1/(2sqrt((1-x)^3))#

Rewrite using negative exponents:

#f(x)=(1-x)^(-1/2)#

Then, applying the Power Rule in conjunction with the Chain Rule,

#f'(x)=-1/2(1-x)^(-3/2)*d/dx(1-x)#

#d/dx(1-x)=-1,# so we have

#f'(x)=1/(2(1-x)^(3/2))#

Rewriting in radical form:

#f'(x)=1/(2sqrt((1-x)^3))#