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

Using quotient rule:

So the solution is: #((x^2+1)x/sqrt(x^2-1) -sqrt(x^2-1)(2x))/(x^2+1)^2 = x/(sqrt(x^2-1) (x^2+1)^2)(x^2+1-2x^2+2) = -x(x^2-3)/(sqrt(x^2-1) (x^2+1)^2)#

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

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

To find the derivative of ( \frac{\sqrt{x^2 - 1}}{x^2 + 1} ), you can use the quotient rule. The quotient rule states that if you have a function ( \frac{u}{v} ), where ( u ) and ( v ) are both functions of ( x ), then the derivative is given by:

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

So applying the quotient rule to ( \frac{\sqrt{x^2 - 1}}{x^2 + 1} ), you get:

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

Now, find the derivatives of ( \sqrt{x^2 - 1} ) and ( x^2 + 1 ), then substitute them into the equation and simplify.

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

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