Question #3b457

1 Answer
turksvids
Jan 16, 2018

#(9(1-x^2))/((7-3x+x^3)^4)#

Explanation:

First let's rewrite the given function:

#f(x) = 1/(7-3x+x^3)^3=(7-3x+x^3)^(-3)#.

By the chain rule #d/dx(g(h(x)))=g'(h(x))*h'(x)#. For this function we have #g(x)=x^-3# and #h(x)=7-3x+x^3#.

#d/dx(f(x)) = -3(7-3x+x^3)^-4*(-3+3x^2)#

#=(9(1-x^2))/((7-3x+x^3)^4)#

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