en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x+5/(x-1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x - 1 ) - 1 \cdot ( x + 5 )}{( x - 1 ) ^{2}} : - \frac{6}{( x - 1 ) ^{2}}

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

Graph

Popular Examples

limit as x approaches 0 of sin((pix)/2)

x \to 0 lim (sin (\frac{π x}{2}))

integral of (3x^2)/(sqrt(x^2-5))

\int \frac{3 x ^{2}}{x ^{2} - 5} d x

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

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

limit as x approaches 9 of 4-sqrt(x)+7

x \to 9 lim (4 - x + 7)

limit as x approaches 0+of (e^{ax}+x)^{1/x}

x \to 0 + lim ((e^{a x} + x)^{\frac{1}{x}})

Frequently Asked Questions (FAQ)

What is the derivative of (x+5/(x-1)) ?
The derivative of (x+5/(x-1)) is -6/((x-1)^2)
What is the first derivative of (x+5/(x-1)) ?
The first derivative of (x+5/(x-1)) is -6/((x-1)^2)