What is the derivative of 1/(x^2-3x) ?

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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