What is (\partial)/(\partial x)(ln(k/x)) ?

The answer to (\partial)/(\partial x)(ln(k/x)) is -1/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(ln(k/x))

\frac{\partial}{\partial x} (ln (\frac{k}{x}))

- \frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{k}{x}))

Apply the chain rule:

\frac{1}{\frac{k}{x}} \frac{\partial}{\partial x} (\frac{k}{x})

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

\frac{\partial}{\partial x} (\frac{k}{x}) = - \frac{k}{x ^{2}}

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

Simplify

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

= - \frac{1}{x}

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

\int e^{5 x} cos (6 x) d x

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

\frac{d}{d x} ((arctan (x))^{2})

\frac{d}{d x} (2 sin (π) x + 3 cos (π) x)

What is (\partial)/(\partial x)(ln(k/x)) ?
The answer to (\partial)/(\partial x)(ln(k/x)) is -1/x