What is the derivative of log_{10}(3x) ?

The derivative of log_{10}(3x) is 1/(ln(10)x)

What is the first derivative of log_{10}(3x) ?

The first derivative of log_{10}(3x) is 1/(ln(10)x)

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derivative of

lo g_{10} (3 x)

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

Solution steps

\frac{d}{d x} (lo g_{10} (3 x))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 3 x )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \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 ( 10 )} \cdot \frac{1}{3 x} \cdot 3

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{3 x} \cdot 3 : \frac{1}{ln ( 10 ) x}

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

\int \frac{1}{( 10 + x ) ^{2}} d x

\int x^{3} 3 - x^{2} d x

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

e^{x} y^{^{'}} = 2 x

\int \frac{4}{x ^{2} + 9} d x

What is the derivative of log_{10}(3x) ?
The derivative of log_{10}(3x) is 1/(ln(10)x)
What is the first derivative of log_{10}(3x) ?
The first derivative of log_{10}(3x) is 1/(ln(10)x)