What is the derivative of log_{8}(sqrt(x)) ?

The derivative of log_{8}(sqrt(x)) is 1/(6ln(2)x)

What is the first derivative of log_{8}(sqrt(x)) ?

The first derivative of log_{8}(sqrt(x)) is 1/(6ln(2)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_{8} (x))

\frac{1}{6 ln ( 2 ) x}

Solution steps

\frac{d}{d x} (lo g_{8} (x))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x )}{ln ( 8 )})

Take the constant out:

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

= \frac{1}{ln ( 8 )} \frac{d}{d x} (ln (x))

Apply the chain rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{1}{ln ( 8 )} \cdot \frac{1}{x} \cdot \frac{1}{2 x}

Simplify

\frac{1}{ln ( 8 )} \cdot \frac{1}{x} \cdot \frac{1}{2 x} : \frac{1}{6 ln ( 2 ) x}

= \frac{1}{6 ln ( 2 ) x}

What is the derivative of log_{8}(sqrt(x)) ?
The derivative of log_{8}(sqrt(x)) is 1/(6ln(2)x)
What is the first derivative of log_{8}(sqrt(x)) ?
The first derivative of log_{8}(sqrt(x)) is 1/(6ln(2)x)