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If #f(x)= x^2-x # and #g(x) = x^( 1/3 ) #, what is #f'(g(x)) #?

1 Answer

A. S. Adikesavan

Dec 21, 2016

#1/3x^(-1/3)(2-x^(-1/3))#

Explanation:

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

#f'(g(x)#

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

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

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

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