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

1 Answer

Jan 16, 2017

#dy/dx=-(8x^3+6)/(x^4+3x)#

Explanation:

If #y=[f(x)]^n#

Then #dy/dx=n[f(x)]^(n-1)f'(x)#

#y=(x^4+3x)^-2#

#dy/dx=-2(x^4+3x)^-3(4x^3+3)=(-2(4x^3+3))/(x^4+3x)^3=-(8x^3+6)/(x^4+3x)^3#

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