en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of x/(x-10)

Solution

\frac{d}{d x} (\frac{x}{x - 10})

Solution

- \frac{10}{( x - 10 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x - 10})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x - 10 ) - \frac{d}{d x} ( x - 10 ) x}{( x - 10 ) ^{2}}

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

\frac{d}{d x} (x - 10) = 1

= \frac{1 \cdot ( x - 10 ) - 1 \cdot x}{( x - 10 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 10 ) - 1 \cdot x}{( x - 10 ) ^{2}} : - \frac{10}{( x - 10 ) ^{2}}

= - \frac{10}{( x - 10 ) ^{2}}

Graph

Popular Examples

(dy)/(dx)=(2x-3)/(5y)

\frac{d y}{d x} = \frac{2 x - 3}{5 y}

derivative of ((x^3-x)/(1+x^2))

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

derivative of ln(((1-x)/((x+5)^3)))

\frac{d}{d x} (ln (\frac{( 1 - x )}{( x + 5 ) ^{3}}))

derivative of cos((pix/2))

\frac{d}{d x} (cos (\frac{π x}{2}))

(\partial)/(\partial x)(6x+12)

\frac{\partial}{\partial x} (6 x + 12)

Frequently Asked Questions (FAQ)

What is the derivative of x/(x-10) ?
The derivative of x/(x-10) is -(10)/((x-10)^2)
What is the first derivative of x/(x-10) ?
The first derivative of x/(x-10) is -(10)/((x-10)^2)