What is the derivative of log_{3}(4x) ?

The derivative of log_{3}(4x) is 1/(ln(3)x)

What is the first derivative of log_{3}(4x) ?

The first derivative of log_{3}(4x) is 1/(ln(3)x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (lo g_{3} (4 x))

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

Solution steps

\frac{d}{d x} (lo g_{3} (4 x))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 4 x )}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (4 x))

Apply the chain rule:

\frac{1}{4 x} \frac{d}{d x} (4 x)

= \frac{1}{4 x} \frac{d}{d x} (4 x)

\frac{d}{d x} (4 x) = 4

= \frac{1}{ln ( 3 )} \cdot \frac{1}{4 x} \cdot 4

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{4 x} \cdot 4 : \frac{1}{ln ( 3 ) x}

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

What is the derivative of log_{3}(4x) ?
The derivative of log_{3}(4x) is 1/(ln(3)x)
What is the first derivative of log_{3}(4x) ?
The first derivative of log_{3}(4x) is 1/(ln(3)x)