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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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