en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (x+2/(x^2-4))

Solution

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

Solution

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

Solution steps

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

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

\frac{d}{d x} (x + 2) = 1

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

= \frac{1 \cdot ( x ^{2} - 4 ) - 2 x ( x + 2 )}{( x ^{2} - 4 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{2} - 4 ) - 2 x ( x + 2 )}{( x ^{2} - 4 ) ^{2}} : - \frac{1}{( x - 2 ) ^{2}}

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

Graph

Popular Examples

derivative of (6x^2+2x+8/(sqrt(x)))

\frac{d}{d x} (\frac{6 x ^{2} + 2 x + 8}{x})

tangent of y=3x^3-x^2+8,(2,28)tangent of

y = 3 x^{3} - x^{2} + 8, (2, 28)

integral of (t^2-2cos(t))

\int (t^{2} - 2 cos (t)) d t

derivative of f(x)=2x^2-3x+1 derivative of

f (x) = 2 x^{2} - 3 x + 1

limit as x approaches 0 of (100)/(x^2)

x \to 0 lim (\frac{100}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of (x+2/(x^2-4)) ?
The derivative of (x+2/(x^2-4)) is -1/((x-2)^2)
What is the first derivative of (x+2/(x^2-4)) ?
The first derivative of (x+2/(x^2-4)) is -1/((x-2)^2)