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How do you use the chain rule to differentiate #f(x)=(x^9+3x^2-5x^-6+3x^4)^-3#?

1 Answer

Jan 24, 2017

#f'(x)=-(3(9x^8+12x^3+6x+30x^-7))/(x^9+3x^4 +3x^2-5x^-6)^4#

Explanation:

#[f(x)]^n=n[f(x)]^(n-1)f'(x)#

#f(x)=(x^9+3x^2-5x^-6+3x^4)^-3#

#f'(x)=-3(x^9+3x^2-5x^-6+3x^4)^-4(9x^8+6x+30x^-7+12x^3)#

#f'(x)=-(3(9x^8+12x^3+6x+30x^-7))/(x^9+3x^4 +3x^2-5x^-6)^4#

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