What is the derivative of (sqrt(x))/(x-1) ?

The derivative of (sqrt(x))/(x-1) is (-x-1)/(2sqrt(x)(x-1)^2)

What is the first derivative of (sqrt(x))/(x-1) ?

The first derivative of (sqrt(x))/(x-1) is (-x-1)/(2sqrt(x)(x-1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x}{x - 1}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

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

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

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

\int_{0}^{1} (x^{2} - 8) e^{- x} d x

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

x^{2} y y^{^{'}} = (y^{2} - 1)^{\frac{3}{2}}

\frac{d}{d x} (x ln (\frac{1}{x}))

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