en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x/(6-x)

Solution

\frac{d}{d x} (\frac{x}{6 - x})

Solution

\frac{6}{( 6 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{6 - x})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 6 - x ) - \frac{d}{d x} ( 6 - x ) x}{( 6 - x ) ^{2}}

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

\frac{d}{d x} (6 - x) = - 1

= \frac{1 \cdot ( 6 - x ) - ( - 1 ) x}{( 6 - x ) ^{2}}

Simplify

\frac{1 \cdot ( 6 - x ) - ( - 1 ) x}{( 6 - x ) ^{2}} : \frac{6}{( 6 - x ) ^{2}}

= \frac{6}{( 6 - x ) ^{2}}

Popular Examples

derivative of y=3x^2+12x+6 derivative of

y = 3 x^{2} + 12 x + 6

limit as x approaches 2 of 8-3x+12x^2

x \to 2 lim (8 - 3 x + 12 x^{2})

derivative of (56/(x^9))

\frac{d}{d x} (\frac{56}{x ^{9}})

integral from 0 to 3 of 1/x

\int_{0}^{3} \frac{1}{x} d x

derivative of (27/((x+5)^{4/3)})

\frac{d}{d x} (\frac{27}{( x + 5 ) ^{\frac{4}{3}}})

Frequently Asked Questions (FAQ)

What is the derivative of x/(6-x) ?
The derivative of x/(6-x) is 6/((6-x)^2)
What is the first derivative of x/(6-x) ?
The first derivative of x/(6-x) is 6/((6-x)^2)