What is the derivative of ((x+3(x+1))/(x^2-49)) ?

The derivative of ((x+3(x+1))/(x^2-49)) is (-4x^2-104x-196)/((x^2-49)^2)

What is the first derivative of ((x+3(x+1))/(x^2-49)) ?

The first derivative of ((x+3(x+1))/(x^2-49)) is (-4x^2-104x-196)/((x^2-49)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{( x + 3 ) ( x + 1 )}{x ^{2} - 49})

\frac{- 4 x ^{2} - 104 x - 196}{( x ^{2} - 49 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x + 3 ) ( x + 1 )}{x ^{2} - 49})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( x + 3 ) ( x + 1 ) ) ( x ^{2} - 49 ) - \frac{d}{d x} ( x ^{2} - 49 ) ( x + 3 ) ( x + 1 )}{( x ^{2} - 49 ) ^{2}}

\frac{d}{d x} ((x + 3) (x + 1)) = 2 x + 4

\frac{d}{d x} (x^{2} - 49) = 2 x

= \frac{( 2 x + 4 ) ( x ^{2} - 49 ) - 2 x ( x + 3 ) ( x + 1 )}{( x ^{2} - 49 ) ^{2}}

Expand

(2 x + 4) (x^{2} - 49) - 2 x (x + 3) (x + 1) : - 4 x^{2} - 104 x - 196

= \frac{- 4 x ^{2} - 104 x - 196}{( x ^{2} - 49 ) ^{2}}

What is the derivative of ((x+3(x+1))/(x^2-49)) ?
The derivative of ((x+3(x+1))/(x^2-49)) is (-4x^2-104x-196)/((x^2-49)^2)
What is the first derivative of ((x+3(x+1))/(x^2-49)) ?
The first derivative of ((x+3(x+1))/(x^2-49)) is (-4x^2-104x-196)/((x^2-49)^2)