What is the derivative of log_{2}(3x+1) ?

The derivative of log_{2}(3x+1) is 3/(ln(2)(3x+1))

What is the first derivative of log_{2}(3x+1) ?

The first derivative of log_{2}(3x+1) is 3/(ln(2)(3x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (lo g_{2} (3 x + 1))

\frac{3}{ln ( 2 ) ( 3 x + 1 )}

Solution steps

\frac{d}{d x} (lo g_{2} (3 x + 1))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 3 x + 1 )}{ln ( 2 )})

Take the constant out:

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

= \frac{1}{ln ( 2 )} \frac{d}{d x} (ln (3 x + 1))

Apply the chain rule:

\frac{1}{3 x + 1} \frac{d}{d x} (3 x + 1)

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

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

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

Simplify

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

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

x y^{^{'}} + y = x

\frac{d}{d x} (\frac{( - 5 x + 1 ) ^{3}}{( 3 x - 3 ) ^{6}})

\frac{\partial}{\partial x} (x^{2} - y^{2} - 2 z^{2})

\frac{d}{d x} (\frac{12 x ^{5} + 8 x ^{3} - 2 x ^{2}}{4 x ^{2}})

\frac{8}{e ^{x} + e ^{- x}}

What is the derivative of log_{2}(3x+1) ?
The derivative of log_{2}(3x+1) is 3/(ln(2)(3x+1))
What is the first derivative of log_{2}(3x+1) ?
The first derivative of log_{2}(3x+1) is 3/(ln(2)(3x+1))