What is the derivative of f(x)=(x+9)/(x-9) ?

The derivative of f(x)=(x+9)/(x-9) is -(18)/((x-9)^2)

What is the first derivative of f(x)=(x+9)/(x-9) ?

The first derivative of f(x)=(x+9)/(x-9) is -(18)/((x-9)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = \frac{x + 9}{x - 9}

- \frac{18}{( x - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 9}{x - 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 9 ) ( x - 9 ) - \frac{d}{d x} ( x - 9 ) ( x + 9 )}{( x - 9 ) ^{2}}

\frac{d}{d x} (x + 9) = 1

\frac{d}{d x} (x - 9) = 1

= \frac{1 \cdot ( x - 9 ) - 1 \cdot ( x + 9 )}{( x - 9 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 9 ) - 1 \cdot ( x + 9 )}{( x - 9 ) ^{2}} : - \frac{18}{( x - 9 ) ^{2}}

= - \frac{18}{( x - 9 ) ^{2}}

What is the derivative of f(x)=(x+9)/(x-9) ?
The derivative of f(x)=(x+9)/(x-9) is -(18)/((x-9)^2)
What is the first derivative of f(x)=(x+9)/(x-9) ?
The first derivative of f(x)=(x+9)/(x-9) is -(18)/((x-9)^2)