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

1 Answer

Leland Adriano Alejandro

Jan 16, 2016

#f' (g(x)) =( -9(x+3)^2)/(2 sqrt(3(x+3)^3 -1)#

Explanation:

#f(x) = -sqrt(3x-1)# and #g(x)=(x+3)^3#

#f(g(x)) = -sqrt(3(g(x))-1)#

#f(g(x))= -sqrt(3(x+3)^3 -1)#

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

#f' (g(x)) =( -9(x+3)^2)/(2 sqrt(3(x+3)^3 -1)#

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