What is the derivative of (ln(3x)/(3x)) ?

The derivative of (ln(3x)/(3x)) is (1-ln(3x))/(3x^2)

What is the first derivative of (ln(3x)/(3x)) ?

The first derivative of (ln(3x)/(3x)) is (1-ln(3x))/(3x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{ln ( 3 x )}{3 x})

\frac{1 - ln ( 3 x )}{3 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{ln ( 3 x )}{3 x})

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} (\frac{ln ( 3 x )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( ln ( 3 x ) ) x - \frac{d x}{d x} ln ( 3 x )}{x ^{2}}

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

\frac{d x}{d x} = 1

= \frac{1}{3} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( 3 x )}{x ^{2}}

Simplify

\frac{1}{3} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( 3 x )}{x ^{2}} : \frac{1 - ln ( 3 x )}{3 x ^{2}}

= \frac{1 - ln ( 3 x )}{3 x ^{2}}

\int \frac{16}{( x + 2 ) ( x ^{2} - 4 )} d x

\int e^{6 x} sin (6 x) d x

\frac{d y}{d x} - y^{2} = 0

(\frac{x ^{2} + 3}{x ^{2} - 3})^{5}

\frac{d}{d x} (\frac{x ^{4}}{2 - x ^{3}})

What is the derivative of (ln(3x)/(3x)) ?
The derivative of (ln(3x)/(3x)) is (1-ln(3x))/(3x^2)
What is the first derivative of (ln(3x)/(3x)) ?
The first derivative of (ln(3x)/(3x)) is (1-ln(3x))/(3x^2)