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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{sin ( x )}{2 x} d x

, x

f (1) = 9 + \frac{3}{x}

f (x) = 3 x + 8

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