What is the derivative of ln(x^{13}) ?

The derivative of ln(x^{13}) is (13)/x

What is the first derivative of ln(x^{13}) ?

The first derivative of ln(x^{13}) is (13)/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 (x^{13}))

\frac{13}{x}

Solution steps

\frac{d}{d x} (ln (x^{13}))

Apply the chain rule:

\frac{1}{x ^{13}} \frac{d}{d x} (x^{13})

= \frac{1}{x ^{13}} \frac{d}{d x} (x^{13})

\frac{d}{d x} (x^{13}) = 13 x^{12}

= \frac{1}{x ^{13}} \cdot 13 x^{12}

Simplify

\frac{1}{x ^{13}} \cdot 13 x^{12} : \frac{13}{x}

= \frac{13}{x}

What is the derivative of ln(x^{13}) ?
The derivative of ln(x^{13}) is (13)/x
What is the first derivative of ln(x^{13}) ?
The first derivative of ln(x^{13}) is (13)/x