What is the derivative of log_{5}(6x^3) ?

The derivative of log_{5}(6x^3) is 3/(ln(5)x)

What is the first derivative of log_{5}(6x^3) ?

The first derivative of log_{5}(6x^3) is 3/(ln(5)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_{5} (6 x^{3}))

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

Solution steps

\frac{d}{d x} (lo g_{5} (6 x^{3}))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 6 x ^{3} )}{ln ( 5 )})

Take the constant out:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (6 x^{3}))

Apply the chain rule:

\frac{1}{6 x ^{3}} \frac{d}{d x} (6 x^{3})

= \frac{1}{6 x ^{3}} \frac{d}{d x} (6 x^{3})

\frac{d}{d x} (6 x^{3}) = 18 x^{2}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{6 x ^{3}} \cdot 18 x^{2}

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{6 x ^{3}} \cdot 18 x^{2} : \frac{3}{ln ( 5 ) x}

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

What is the derivative of log_{5}(6x^3) ?
The derivative of log_{5}(6x^3) is 3/(ln(5)x)
What is the first derivative of log_{5}(6x^3) ?
The first derivative of log_{5}(6x^3) is 3/(ln(5)x)