What is the derivative of x/(x^2+14x+45) ?

The derivative of x/(x^2+14x+45) is (-x^2+45)/((x^2+14x+45)^2)

What is the first derivative of x/(x^2+14x+45) ?

The first derivative of x/(x^2+14x+45) is (-x^2+45)/((x^2+14x+45)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{x}{x ^{2} + 14 x + 45}

\frac{- x ^{2} + 45}{( x ^{2} + 14 x + 45 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 14 x + 45})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 14 x + 45 ) - \frac{d}{d x} ( x ^{2} + 14 x + 45 ) x}{( x ^{2} + 14 x + 45 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 14 x + 45) = 2 x + 14

= \frac{1 \cdot ( x ^{2} + 14 x + 45 ) - ( 2 x + 14 ) x}{( x ^{2} + 14 x + 45 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{2} + 14 x + 45 ) - ( 2 x + 14 ) x}{( x ^{2} + 14 x + 45 ) ^{2}} : \frac{- x ^{2} + 45}{( x ^{2} + 14 x + 45 ) ^{2}}

= \frac{- x ^{2} + 45}{( x ^{2} + 14 x + 45 ) ^{2}}

What is the derivative of x/(x^2+14x+45) ?
The derivative of x/(x^2+14x+45) is (-x^2+45)/((x^2+14x+45)^2)
What is the first derivative of x/(x^2+14x+45) ?
The first derivative of x/(x^2+14x+45) is (-x^2+45)/((x^2+14x+45)^2)