What is the derivative of ln(1/(6+x)) ?

The derivative of ln(1/(6+x)) is -1/(6+x)

What is the first derivative of ln(1/(6+x)) ?

The first derivative of ln(1/(6+x)) is -1/(6+x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (ln (\frac{1}{6 + x}))

- \frac{1}{6 + x}

Solution steps

\frac{d}{d x} (ln (\frac{1}{6 + x}))

Simplify

ln (\frac{1}{6 + x}) : - ln (6 + x)

= \frac{d}{d x} (- ln (6 + x))

Take the constant out:

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

= - \frac{d}{d x} (ln (6 + x))

Apply the chain rule:

\frac{1}{6 + x} \frac{d}{d x} (6 + x)

= \frac{1}{6 + x} \frac{d}{d x} (6 + x)

\frac{d}{d x} (6 + x) = 1

= - \frac{1}{6 + x} \cdot 1

Simplify

= - \frac{1}{6 + x}

What is the derivative of ln(1/(6+x)) ?
The derivative of ln(1/(6+x)) is -1/(6+x)
What is the first derivative of ln(1/(6+x)) ?
The first derivative of ln(1/(6+x)) is -1/(6+x)