How do you find the derivative of x/(1+x^2)?

1 Answer
Jan 8, 2016

(1-x^2)/(1+x^2)^2

Explanation:

Use the quotient rule, which states that for a function

f(x)=(g(x))/(h(x))

the derivative of the function is

f'(x)=(g'(x)h(x)-h'(x)g(x))/(h(x))^2

Thus, the derivative of x/(1+x^2) is

((1+x^2)d/dx(x)-xd/dx(1+x^2))/(1+x^2)^2

Find each derivative.

d/dx(x)=1

d/dx(1+x^2)=2x

Hence the derivative is equal to

((1+x^2)-x(2x))/(1+x^2)^2

=(1-x^2)/(1+x^2)^2