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

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

To find the derivative of ( \frac{1}{1+x^2} ), you can use the quotient rule. The quotient rule states that if you have a function in the form ( \frac{u}{v} ), then the derivative is given by ( \frac{u'v - uv'}{v^2} ), where ( u' ) and ( v' ) represent the derivatives of ( u ) and ( v ) respectively.

For the given function ( \frac{1}{1+x^2} ), let ( u = 1 ) and ( v = 1 + x^2 ).

Now, differentiate both ( u ) and ( v ) with respect to ( x ).

( u' = 0 ) (since the derivative of a constant is zero)

( v' = 2x )

Now, apply the quotient rule:

( \frac{d}{dx} \left( \frac{1}{1+x^2} \right) = \frac{(0)(1+x^2) - (1)(2x)}{(1+x^2)^2} )

Simplifying, we get:

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