How do you use the chain rule to differentiate #f(x)=(3x-9)^2(4x^3+2x^-9)^-9#?

1 Answer
Oct 21, 2017

Answer:

see below

Explanation:

#f(x)=(3x-9)^2(4x^3+2x^-9)^-9#

#f'(x)=(3x-9)^2d/dy(4x^3+2x^-9)^-9+(4x^3+2x^-9)^-9d/dx(3x-9)^2#

#=(3x-9)^2(-9)(4x^3+2x^-9)^-10d/dy(4x^3+2x^-9)+(4x^3+2x^-9)^-9(2)(3x-9)d/dx(3x-9)#

#=(3x-9)^2(-9)(4x^3+2x^-9)^-10(12x^2-18x^-10)+(4x^3+2x^-9)^-9(2)(3x-9)(3)#

#=(-9)(3x-9)^2(4x^3+2x^-9)^-10(12x^2-18x^-10)+(6)(4x^3+2x^-9)^-9(3x-9)#