What is the derivative of log_{5}(2x) ?

The derivative of log_{5}(2x) is 1/(ln(5)x)

What is the first derivative of log_{5}(2x) ?

The first derivative of log_{5}(2x) is 1/(ln(5)x)

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derivative of

lo g_{5} (2 x)

\frac{1}{ln ( 5 ) x}

Solution steps

\frac{d}{d x} (lo g_{5} (2 x))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 2 x )}{ln ( 5 )})

Take the constant out:

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

= \frac{1}{ln ( 5 )} \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 ( 5 )} \cdot \frac{1}{2 x} \cdot 2

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{2 x} \cdot 2 : \frac{1}{ln ( 5 ) x}

= \frac{1}{ln ( 5 ) x}

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What is the derivative of log_{5}(2x) ?
The derivative of log_{5}(2x) is 1/(ln(5)x)
What is the first derivative of log_{5}(2x) ?
The first derivative of log_{5}(2x) is 1/(ln(5)x)