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

The derivative of ln((xln(x-1)/(xln(x)+1))) is (2ln(x)+2)/((xln(x)-1)(xln(x)+1))

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

The first derivative of ln((xln(x-1)/(xln(x)+1))) is (2ln(x)+2)/((xln(x)-1)(xln(x)+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = \frac{( x + 1 )}{( x - 1 )}

\frac{3 t - 1}{t - 2}

\frac{\partial}{\partial x} (\frac{x}{2 y})

\int \frac{2}{cos ( x )} e^{2 l n (c o s (x))} d x

\int_{1}^{x} \frac{2}{x ^{3}} d x

What is the derivative of ln((xln(x-1)/(xln(x)+1))) ?
The derivative of ln((xln(x-1)/(xln(x)+1))) is (2ln(x)+2)/((xln(x)-1)(xln(x)+1))
What is the first derivative of ln((xln(x-1)/(xln(x)+1))) ?
The first derivative of ln((xln(x-1)/(xln(x)+1))) is (2ln(x)+2)/((xln(x)-1)(xln(x)+1))