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

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

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

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

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Popular >

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

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(1 + x)^{- 3}

\int \frac{x}{x ^{2} + x + 2} d x

\int (12 x^{2} - 8 x + 5) d x

\int 7 t d t

\frac{\partial}{\partial y} (x^{2} - x y + 5 y^{2})

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