How do you differentiate #f(x)=(5x-2)/(x^2+1)# using the quotient rule?

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Answer 1 · 2018-03-15T09:41:14

See explanation.

The Quotient Rule says that

#[f(x)/g(x)]^'=(f^'(x)*g(x)-f(x)g^'(x))/[[g(x)]^2]#

In the given example we have:

#f(x)=5x-2#

#f'(x)=5#

#g(x)=x^2+1#

#g'(x)=2x#

So the derivative is:

#[(5x-2)/(x^2+1)]^'=(5(x^2+1)-(5x-2)*(2x))/(x^2+1)^2#

#[(5x-2)/(x^2+1)]^'=(5x^2+5-10x^2+4x)/(x^2+1)^2#

#[(5x-2)/(x^2+1)]^'=(-5x^2+4x+5)/(x^2+1)^2#