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

The answer to (\partial)/(\partial x)(ln(a/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(a/x))

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

- \frac{1}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{x}

\int_{0}^{5} 5 d x

n = 6 \sum \infty \frac{5}{n ^{2} - 25}

\frac{d}{d x} ((x^{2}) (y^{2} - 9))

\frac{x}{3}

\int (- 4 x^{6} - 3 x^{5} + 5 e^{x}) d x

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