en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x/(x-5)

Solution

derivative of

\frac{x}{x - 5}

Solution

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

Solution steps

\frac{d}{d x} (\frac{x}{x - 5})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 5) = 1

= \frac{1 \cdot ( x - 5 ) - 1 \cdot x}{( x - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 5 ) - 1 \cdot x}{( x - 5 ) ^{2}} : - \frac{5}{( x - 5 ) ^{2}}

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

Graph

Popular Examples

slope of (3.2)(5.6)slope

(3.2) (5.6)

derivative of y=(x-2)(2x+3)derivative of

y = (x - 2) (2 x + 3)

derivative of sqrt(12-x)

\frac{d}{d x} (12 - x)

limit as x approaches infinity of (x^3)/(1e^{x/2)}

x \to \infty lim (\frac{x ^{3}}{1 e ^{\frac{x}{2}}})

integral of 2x^3sqrt(x^4+2)

\int 2 x^{3} x^{4} + 2 d x

Frequently Asked Questions (FAQ)

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