en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (1-sqrt(x)^{-1})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=(4x^2+5)(2x-3)derivative of

y = (4 x^{2} + 5) (2 x - 3)

\frac{d}{d j} (3 i - 4 j)

(dy)/(dx)+3tan(3x)y=-5cos(3x)

\frac{d y}{d x} + 3 tan (3 x) y = - 5 cos (3 x)

limit as x approaches 0 of x

x \to 0 lim (x)

sum from n=0 to infinity of (-1^n)/(n+2)

n = 0 \sum \infty \frac{- 1 ^{n}}{n + 2}

Frequently Asked Questions (FAQ)

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