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

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

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

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

Popular >

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

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x}, y^{3} = 2 x

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 9

\frac{d}{d x} (\frac{x + 3}{x ^{2}})

\int_{- 2}^{1} (4 - x^{2}) - (x + 2) d x

f (x) = (5 x^{2} - 8 x) e^{x}

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