en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/(x^2-x)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of-2e^{x^2}sin(2y)+(x^2)/2+1

\int - 2 e^{x^{2}} sin (2 y) + \frac{x ^{2}}{2} + 1

taylor 4+x^2+4x^4,3 taylor

4 + x^{2} + 4 x^{4}, 3

integral of (7e^{3t})/(1+e^{6t)}

\int \frac{7 e ^{3 t}}{1 + e ^{6 t}} d t

area 2x^2+3,-1,2 area

2 x^{2} + 3, - 1, 2

integral of x/(sqrt(x^2+36))

\int \frac{x}{x ^{2} + 36} d x

Frequently Asked Questions (FAQ)

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