What is the derivative of (ln(x)^5) ?

The derivative of (ln(x)^5) is (5ln^4(x))/x

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

The first derivative of (ln(x)^5) is (5ln^4(x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{5 ln ^{4} ( x )}{x}

Solution steps

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

Apply the chain rule:

5 (ln (x))^{4} \frac{d}{d x} (ln (x))

= 5 (ln (x))^{4} \frac{d}{d x} (ln (x))

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

= 5 (ln (x))^{4} \frac{1}{x}

Simplify

5 ln^{4} (x) \frac{1}{x} : \frac{5 ln ^{4} ( x )}{x}

= \frac{5 ln ^{4} ( x )}{x}

\int 8 x e^{8 x} d x

ln^{3} (x)

\frac{d y}{d x} = \frac{( 1 - 3 y ) ^{2}}{x}, y (1) = 1

\frac{d}{d x} ((x^{2} + 1)^{2})

n = 0 \sum \infty \frac{n ^{2}}{n !}

What is the derivative of (ln(x)^5) ?
The derivative of (ln(x)^5) is (5ln^4(x))/x
What is the first derivative of (ln(x)^5) ?
The first derivative of (ln(x)^5) is (5ln^4(x))/x