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

The derivative of (-1x+sqrt(1+x)/(x^2-1)) is (2x^2-3xsqrt(x+1)-sqrt(x+1)+2)/(2(x^2-1)^2)

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

The first derivative of (-1x+sqrt(1+x)/(x^2-1)) is (2x^2-3xsqrt(x+1)-sqrt(x+1)+2)/(2(x^2-1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 1 + \frac{1}{2 1 + x} ) ( x ^{2} - 1 ) - 2 x ( - 1 \cdot x + 1 + x )}{( x ^{2} - 1 ) ^{2}} : \frac{2 x ^{2} - 3 x x + 1 - x + 1 + 2}{2 ( x ^{2} - 1 ) ^{2}}

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

What is the derivative of (-1x+sqrt(1+x)/(x^2-1)) ?
The derivative of (-1x+sqrt(1+x)/(x^2-1)) is (2x^2-3xsqrt(x+1)-sqrt(x+1)+2)/(2(x^2-1)^2)
What is the first derivative of (-1x+sqrt(1+x)/(x^2-1)) ?
The first derivative of (-1x+sqrt(1+x)/(x^2-1)) is (2x^2-3xsqrt(x+1)-sqrt(x+1)+2)/(2(x^2-1)^2)