What is the derivative of log_{10}(7x) ?

The derivative of log_{10}(7x) is 1/(ln(10)x)

What is the first derivative of log_{10}(7x) ?

The first derivative of log_{10}(7x) is 1/(ln(10)x)

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\frac{d}{d x} (lo g_{10} (7 x))

\frac{1}{ln ( 10 ) x}

Solution steps

\frac{d}{d x} (lo g_{10} (7 x))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 7 x )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (7 x))

Apply the chain rule:

\frac{1}{7 x} \frac{d}{d x} (7 x)

= \frac{1}{7 x} \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x) = 7

= \frac{1}{ln ( 10 )} \cdot \frac{1}{7 x} \cdot 7

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{7 x} \cdot 7 : \frac{1}{ln ( 10 ) x}

= \frac{1}{ln ( 10 ) x}

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What is the derivative of log_{10}(7x) ?
The derivative of log_{10}(7x) is 1/(ln(10)x)
What is the first derivative of log_{10}(7x) ?
The first derivative of log_{10}(7x) is 1/(ln(10)x)