# How do you use the Quotient Rule to differentiate the function #f(x)=(x)/(x^2+1)#?

I found:

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

To differentiate the function ( f(x) = \frac{x}{x^2 + 1} ) using the Quotient Rule:

- Identify the numerator ( u(x) = x ) and the denominator ( v(x) = x^2 + 1 ).
- Apply the Quotient Rule formula: [ f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2} ]
- Compute the derivatives:
- ( u'(x) = 1 ) (derivative of ( x )).
- ( v'(x) = 2x ) (derivative of ( x^2 + 1 )).

- Plug the derivatives and the original functions into the Quotient Rule formula: [ f'(x) = \frac{(1)(x^2 + 1) - (x)(2x)}{(x^2 + 1)^2} ]
- Simplify the expression: [ f'(x) = \frac{x^2 + 1 - 2x^2}{(x^2 + 1)^2} ] [ f'(x) = \frac{-x^2 + 1}{(x^2 + 1)^2} ]

So, the derivative of ( f(x) = \frac{x}{x^2 + 1} ) with respect to ( x ) is ( f'(x) = \frac{-x^2 + 1}{(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