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 >

\frac{d}{d x} (\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}}

\int x^{3} (1 + 9 x^{4}) d x

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

\int 6 x^{13} e^{- x^{7}} d x

x \to 0 lim (\frac{4}{1 + 2 ^{\frac{1}{x}}})

\frac{d}{d x} (4 cos (4 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)