How do you use the chain rule to differentiate $y=((5x^5-3)/(-3x^3+1))^3$ ?

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Answer 1 · 2018-02-24T15:25:32

$y= ((5x^2 - 3)/ (-3x^3+1))^3$

$dy/dx= 3((5x^2 - 3)/ (-3x^3+1))^2 xx (d((5x^2 - 3)/ (-3x^3+1)))/dx$

$dy/dx= 3((5x^2 - 3)/ (-3x^3+1))^2 xx [((5x^2 - 3)'(-3x^3+1)-(5x^2 - 3)(-3x^3+1)')/(-3x^3+1)^2]$

$dy/dx= 3((5x^2 - 3)/ (-3x^3+1))^2 xx [(10x(-3x^3+1)-(5x^2 - 3)(-9x^2))/(-3x^3+1)^2]$

How do you use the chain rule to differentiate y=((5x^5-3)/(-3x^3+1))^3y=((5x^5-3)/(-3x^3+1))^3?