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

The derivative of (sqrt(x)-1)/(sqrt(x)+1) is 1/(sqrt(x)(\sqrt{x)+1)^2}

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

The first derivative of (sqrt(x)-1)/(sqrt(x)+1) is 1/(sqrt(x)(\sqrt{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 - 1}{x + 1}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{cos ( x )}{2 sin ( x ) + 1} d x

\int x \cdot (4 - x) d x

5 + 4 δ (t)

\int 4^{s i n (x)} cos (x) d x

x \to - 7 lim (\frac{x + 8}{x + 7})

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