How do you differentiate #f(x)=sqrt(1/(3x-2))# using the chain rule?

1 Answer
Vikki
Dec 5, 2015

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

Explanation:

Rewire the expression using the rational exponential rule

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

Rewrite using power rule of exponent
#f(x) = (3x-2)^(-1/2)#

Begin to find the derivative
#f'(x) = -1/2 (3x-2)^(-1/2 -1)*3#

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

Rewrite without negative exponent
#f'(x) = -1/[2(3x-2)^(3/2)]#

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