What is the derivative of k/x ?

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

What is the first derivative of k/x ?

The first derivative of k/x is -k/(x^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{k}{x})

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= k (- 1 \cdot x^{- 1 - 1})

Simplify

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

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