Question

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

Answer 1

`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]`