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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{z + 1}{z - 1}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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