What is the derivative of (x^2+5x+6)/(x^2-4) ?

The derivative of (x^2+5x+6)/(x^2-4) is -5/((x-2)^2)

What is the first derivative of (x^2+5x+6)/(x^2-4) ?

The first derivative of (x^2+5x+6)/(x^2-4) is -5/((x-2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x ^{2} + 5 x + 6}{x ^{2} - 4}

- \frac{5}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 5 x + 6}{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} + 5 x + 6 ) ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) ( x ^{2} + 5 x + 6 )}{( x ^{2} - 4 ) ^{2}}

\frac{d}{d x} (x^{2} + 5 x + 6) = 2 x + 5

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

= \frac{( 2 x + 5 ) ( x ^{2} - 4 ) - 2 x ( x ^{2} + 5 x + 6 )}{( x ^{2} - 4 ) ^{2}}

Simplify

\frac{( 2 x + 5 ) ( x ^{2} - 4 ) - 2 x ( x ^{2} + 5 x + 6 )}{( x ^{2} - 4 ) ^{2}} : - \frac{5}{( x - 2 ) ^{2}}

= - \frac{5}{( x - 2 ) ^{2}}

\frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{2}}

\int \frac{1}{aa uu} d u

\frac{d}{d x} (\frac{1}{sin ( x ^{2} )})

\int e^{4 x} cos (3 x) d x

\frac{\partial}{\partial x} (y + e^{x})

What is the derivative of (x^2+5x+6)/(x^2-4) ?
The derivative of (x^2+5x+6)/(x^2-4) is -5/((x-2)^2)
What is the first derivative of (x^2+5x+6)/(x^2-4) ?
The first derivative of (x^2+5x+6)/(x^2-4) is -5/((x-2)^2)