How do you differentiate f(x)=(5x-2)/(x^2+1)f(x)=5x2x2+1 using the quotient rule?

1 Answer
Mar 15, 2018

See explanation.

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