What is the derivative of (12x)/(x^2-4) ?

The derivative of (12x)/(x^2-4) is (12(-x^2-4))/((x^2-4)^2)

What is the first derivative of (12x)/(x^2-4) ?

The first derivative of (12x)/(x^2-4) is (12(-x^2-4))/((x^2-4)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{12 x}{x ^{2} - 4}

\frac{12 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{12 x}{x ^{2} - 4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d x} (\frac{x}{x ^{2} - 4})

Apply the Quotient Rule:

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

= 12 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) x}{( x ^{2} - 4 ) ^{2}}

\frac{d x}{d x} = 1

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

= 12 \cdot \frac{1 \cdot ( x ^{2} - 4 ) - 2 xx}{( x ^{2} - 4 ) ^{2}}

Simplify

12 \cdot \frac{1 \cdot ( x ^{2} - 4 ) - 2 xx}{( x ^{2} - 4 ) ^{2}} : \frac{12 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}}

= \frac{12 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}}

x \to \infty lim (\frac{0}{3})

f (x) = \frac{x}{x ^{3} + 1}

\int (6 x - x^{2}) d x

\int \frac{3}{x ^{2} + 16} d x

\int 5 x^{- 4} d x

What is the derivative of (12x)/(x^2-4) ?
The derivative of (12x)/(x^2-4) is (12(-x^2-4))/((x^2-4)^2)
What is the first derivative of (12x)/(x^2-4) ?
The first derivative of (12x)/(x^2-4) is (12(-x^2-4))/((x^2-4)^2)