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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{2}{x + 2}

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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