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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{1}^{8} 9 \frac{ln ( x )}{x ^{2}} d x

x^{x^{2}}, 1

\frac{1}{x x ^{2} - 1}

\frac{\partial}{\partial x} (7 cos (x) sin (y))

\frac{d}{d x} (\frac{e ^{3 x}}{x})

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