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

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

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

The first derivative of (2-x/(x^2+4)) is (x^2-4x-4)/((x^2+4)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int_{0}^{\frac{3}{2}} 9 - x^{2} d x

\int x^{2} (3 x^{2} + 9)^{2} d x

\int csc^{3} (x) cot^{3} (x) d x

x \to \infty lim (\frac{1}{1 0 ^{2^{x}}})

\frac{d}{d j} (- 4 i + 5 j)

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