What is the derivative of f(x)=arctan((x-1)/(x+1)) ?

The derivative of f(x)=arctan((x-1)/(x+1)) is 1/(x^2+1)

What is the first derivative of f(x)=arctan((x-1)/(x+1)) ?

The first derivative of f(x)=arctan((x-1)/(x+1)) is 1/(x^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d ^{2}}{d x ^{2}} (x^{2} e^{- x})

\frac{d h}{d t} = - h^{3}

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

\frac{d}{d x} (e^{\frac{in x}{2 x}})

\int \frac{sin ( 2 θ )}{cos ( 2 θ )} d θ

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