en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^2/(x^2-2))

Solution

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 2})

Solution

- \frac{4 x}{( x ^{2} - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 2})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} - 2 ) - \frac{d}{d x} ( x ^{2} - 2 ) x ^{2}}{( x ^{2} - 2 ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (x^{2} - 2) = 2 x

= \frac{2 x ( x ^{2} - 2 ) - 2 x x ^{2}}{( x ^{2} - 2 ) ^{2}}

Simplify

\frac{2 x ( x ^{2} - 2 ) - 2 x x ^{2}}{( x ^{2} - 2 ) ^{2}} : - \frac{4 x}{( x ^{2} - 2 ) ^{2}}

= - \frac{4 x}{( x ^{2} - 2 ) ^{2}}

Popular Examples

(\partial)/(\partial x)((6-x-y)^2)

\frac{\partial}{\partial x} ((6 - x - y)^{2})

(dy)/(dt)=-2(y-3)

\frac{d y}{d t} = - 2 (y - 3)

(\partial)/(\partial x)(17xye^{-x^2-y^2})

\frac{\partial}{\partial x} (17 x y e^{- x^{2} - y^{2}})

(\partial)/(\partial x)(c(1+m*x)-c(1+m)^x)

\frac{\partial}{\partial x} (c (1 + m \cdot x) - c (1 + m)^{x})

sum from n=1 to infinity of n/(3n^3+1)

n = 1 \sum \infty \frac{n}{3 n ^{3} + 1}

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(x^2-2)) ?
The derivative of (x^2/(x^2-2)) is -(4x)/((x^2-2)^2)
What is the first derivative of (x^2/(x^2-2)) ?
The first derivative of (x^2/(x^2-2)) is -(4x)/((x^2-2)^2)