# What is the derivative of #(x/(x^2+1))#?

We can proceed to derivate this with no big problems.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of the function ( \frac{x}{x^2 + 1} ), you can use the quotient rule, which states that if you have a function ( \frac{u(x)}{v(x)} ), the derivative is given by:

[ \frac{d}{dx} \left( \frac{u(x)}{v(x)} \right) = \frac{v(x) \cdot u'(x) - u(x) \cdot v'(x)}{(v(x))^2} ]

Using this rule, where ( u(x) = x ) and ( v(x) = x^2 + 1 ), we can compute the derivative as follows:

[ \frac{d}{dx} \left( \frac{x}{x^2 + 1} \right) = \frac{(x^2 + 1) \cdot (1) - (x) \cdot (2x)}{(x^2 + 1)^2} ]

[ = \frac{x^2 + 1 - 2x^2}{(x^2 + 1)^2} ]

[ = \frac{1 - x^2}{(x^2 + 1)^2} ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7