What is the derivative of ln(x/(sqrt(x^2+1))) ?

The derivative of ln(x/(sqrt(x^2+1))) is 1/(x(x^2+1))

What is the first derivative of ln(x/(sqrt(x^2+1))) ?

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (m sin (2 (m x + n y)))

\int_{2}^{e} \frac{1}{x ln ( x )} d x

f (x) = x (5 x^{5} - 1)

\int x sin (9 x^{2}) d x

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