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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int coth^{2} (x) d x

\int \frac{1}{9 - x ^{2}} d x

\int e^{- k N x} d x

2 (x - 6)^{3}

z \to 0 lim (z^{3} cos (\frac{1}{z}))

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