en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(2x+5)/(x-1)

Solution

derivative of

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

Solution

- \frac{7}{( x - 1 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{2 ( x - 1 ) - 1 \cdot ( 2 x + 5 )}{( x - 1 ) ^{2}} : - \frac{7}{( x - 1 ) ^{2}}

= - \frac{7}{( x - 1 ) ^{2}}

Popular Examples

integral of 1/(x^4sqrt(16x^2-9))

\int \frac{1}{x ^{4} 16 x ^{2} - 9} d x

limit as x approaches infinity of 4/x-5

x \to \infty lim (\frac{4}{x} - 5)

tangent of y=sqrt(3x+7),(6,5)tangent of

y = 3 x + 7, (6, 5)

derivative of y=2x^3+3x^2-12x+8 derivative of

y = 2 x^{3} + 3 x^{2} - 12 x + 8

integral of 13x^3e^x

\int 13 x^{3} e^{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2x+5)/(x-1) ?
The derivative of f(x)=(2x+5)/(x-1) is -7/((x-1)^2)
What is the first derivative of f(x)=(2x+5)/(x-1) ?
The first derivative of f(x)=(2x+5)/(x-1) is -7/((x-1)^2)