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

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Mr.X Share
Oct 21, 2017

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see below

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#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)#

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