If #f(x)= (5x -1)^3 # and #g(x) = 3x^( 2/3 ) #, what is #f'(g(x)) #?

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Answer 1 · 2017-01-26T07:58:44

Given #f(x)= (5x -1)^3 # and #g(x) = 3x^( 2/3 ) #,

we get

#f(g(x)) =(5(g(x))-1)^3 #

#f(g(x)) =(5*3x^(2/3)-1)^3 #

#=>f(g(x)) =(15x^(2/3)-1)^3 #

#=>f'(g(x)) =3(15x^(2/3)-1)^2xx(15*2/3x^(2/3-1)) #

#=>f'(g(x)) =3(15x^(2/3)-1)^2xx(10x^(-1/3)) #

#=>f'(g(x)) =(30(15x^(2/3)-1)^2)/x^(1/3) #