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

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

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

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

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})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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