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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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