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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 \frac{l n ( x ) + 1}{l n ( x ) - 1}} (- \frac{2}{x ( ln ( x ) - 1 ) ^{2}}) : - \frac{1}{x ln ( x ) + 1 ( ln ( x ) - 1 ) ^{\frac{3}{2}}}

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

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