What is (\partial)/(\partial x)(ln(x/(20))) ?

The answer to (\partial)/(\partial x)(ln(x/(20))) is 1/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(ln(x/(20)))

\frac{\partial}{\partial x} (ln (\frac{x}{20}))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{x}{20}))

Apply the chain rule:

\frac{1}{\frac{x}{20}} \frac{\partial}{\partial x} (\frac{x}{20})

= \frac{1}{\frac{x}{20}} \frac{\partial}{\partial x} (\frac{x}{20})

\frac{\partial}{\partial x} (\frac{x}{20}) = \frac{1}{20}

= \frac{1}{\frac{x}{20}} \cdot \frac{1}{20}

Simplify

\frac{1}{\frac{x}{20}} \cdot \frac{1}{20} : \frac{1}{x}

= \frac{1}{x}

What is (\partial)/(\partial x)(ln(x/(20))) ?
The answer to (\partial)/(\partial x)(ln(x/(20))) is 1/x