What is the derivative of ln(x/y) ?

The derivative of ln(x/y) is 1/x

What is the first derivative of ln(x/y) ?

The first derivative of ln(x/y) is 1/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

ln (\frac{x}{y})

\frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{x}{y}))

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

What is the derivative of ln(x/y) ?
The derivative of ln(x/y) is 1/x
What is the first derivative of ln(x/y) ?
The first derivative of ln(x/y) is 1/x