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

The derivative of 1/(sqrt(2+x)) is -1/(2(2+x)^{3/2)}

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

The first derivative of 1/(sqrt(2+x)) is -1/(2(2+x)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

What is the derivative of 1/(sqrt(2+x)) ?
The derivative of 1/(sqrt(2+x)) is -1/(2(2+x)^{3/2)}
What is the first derivative of 1/(sqrt(2+x)) ?
The first derivative of 1/(sqrt(2+x)) is -1/(2(2+x)^{3/2)}