What is the derivative of log_{3}(5x-1) ?

The derivative of log_{3}(5x-1) is 5/(ln(3)(5x-1))

What is the first derivative of log_{3}(5x-1) ?

The first derivative of log_{3}(5x-1) is 5/(ln(3)(5x-1))

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} (5 x - 1))

\frac{5}{ln ( 3 ) ( 5 x - 1 )}

Solution steps

\frac{d}{d x} (lo g_{3} (5 x - 1))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 5 x - 1 )}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (5 x - 1))

Apply the chain rule:

\frac{1}{5 x - 1} \frac{d}{d x} (5 x - 1)

= \frac{1}{5 x - 1} \frac{d}{d x} (5 x - 1)

\frac{d}{d x} (5 x - 1) = 5

= \frac{1}{ln ( 3 )} \cdot \frac{1}{5 x - 1} \cdot 5

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{5 x - 1} \cdot 5 : \frac{5}{ln ( 3 ) ( 5 x - 1 )}

= \frac{5}{ln ( 3 ) ( 5 x - 1 )}

What is the derivative of log_{3}(5x-1) ?
The derivative of log_{3}(5x-1) is 5/(ln(3)(5x-1))
What is the first derivative of log_{3}(5x-1) ?
The first derivative of log_{3}(5x-1) is 5/(ln(3)(5x-1))