How do you find the derivative using quotient rule of #[x(3x+5)] / (1-x^2)#?

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Answer 1 · 2016-01-24T21:49:36

#f'(x)=(5x^2+6x+5)/(1-x^2)^2#

First, simplify the numerator.

#f(x)=(3x^2+5x)/(1-x^2)#

Now, according to the quotient rule,

#f'(x)=((1-x^2)d/dx(3x^2+5x)-(3x^2+5x)d/dx(1-x^2))/(1-x^2)^2#

Find each derivative through the power rule.

#f'(x)=((1-x^2)(6x+5)-(3x^2+5x)(-2x))/(1-x^2)^2#

Distribute and simplify.

#f'(x)=(-6x^3-5x^2+6x+5+6x^3+10x^2)/(1-x^2)^2#

#f'(x)=(5x^2+6x+5)/(1-x^2)^2#