What is the derivative of (ln(x))^6 ?

The derivative of (ln(x))^6 is (6ln^5(x))/x

What is the first derivative of (ln(x))^6 ?

The first derivative of (ln(x))^6 is (6ln^5(x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

(ln (x))^{6}

\frac{6 ln ^{5} ( x )}{x}

Solution steps

\frac{d}{d x} ((ln (x))^{6})

Apply the chain rule:

6 (ln (x))^{5} \frac{d}{d x} (ln (x))

= 6 (ln (x))^{5} \frac{d}{d x} (ln (x))

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

= 6 (ln (x))^{5} \frac{1}{x}

Simplify

6 ln^{5} (x) \frac{1}{x} : \frac{6 ln ^{5} ( x )}{x}

= \frac{6 ln ^{5} ( x )}{x}

What is the derivative of (ln(x))^6 ?
The derivative of (ln(x))^6 is (6ln^5(x))/x
What is the first derivative of (ln(x))^6 ?
The first derivative of (ln(x))^6 is (6ln^5(x))/x