What is the derivative of arctan((3+x/(3-x))) ?

The derivative of arctan((3+x/(3-x))) is 3/(x^2+9)

What is the first derivative of arctan((3+x/(3-x))) ?

The first derivative of arctan((3+x/(3-x))) is 3/(x^2+9)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (arctan (\frac{3 + x}{3 - x}))

\frac{3}{x ^{2} + 9}

Solution steps

\frac{d}{d x} (arctan (\frac{3 + x}{3 - x}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 + x}{3 - x}) = \frac{6}{( 3 - x ) ^{2}}

= \frac{1}{( \frac{3 + x}{3 - x} ) ^{2} + 1} \cdot \frac{6}{( 3 - x ) ^{2}}

Simplify

\frac{1}{( \frac{3 + x}{3 - x} ) ^{2} + 1} \cdot \frac{6}{( 3 - x ) ^{2}} : \frac{3}{x ^{2} + 9}

= \frac{3}{x ^{2} + 9}

What is the derivative of arctan((3+x/(3-x))) ?
The derivative of arctan((3+x/(3-x))) is 3/(x^2+9)
What is the first derivative of arctan((3+x/(3-x))) ?
The first derivative of arctan((3+x/(3-x))) is 3/(x^2+9)