What is the derivative of 1/x ?

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

What is the first derivative of 1/x ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{1}{x}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= - 1 \cdot x^{- 1 - 1}

Simplify

- 1 \cdot x^{- 1 - 1} : - \frac{1}{x ^{2}}

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

y = 2 x, y = 9 x^{2}

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x ^{5}})

\int sin (x) sin (2 x) sin (3 x) d x

\frac{d}{d x} (- 18 x - \frac{17}{x})

\frac{y ^{3}}{9} + \frac{3}{4 y}