What is the derivative of log_{10}(4x) ?

The derivative of log_{10}(4x) is 1/(ln(10)x)

What is the first derivative of log_{10}(4x) ?

The first derivative of log_{10}(4x) is 1/(ln(10)x)

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\frac{d}{d x} (lo g_{10} (4 x))

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

Solution steps

\frac{d}{d x} (lo g_{10} (4 x))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 4 x )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (4 x))

Apply the chain rule:

\frac{1}{4 x} \frac{d}{d x} (4 x)

= \frac{1}{4 x} \frac{d}{d x} (4 x)

\frac{d}{d x} (4 x) = 4

= \frac{1}{ln ( 10 )} \cdot \frac{1}{4 x} \cdot 4

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{4 x} \cdot 4 : \frac{1}{ln ( 10 ) x}

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

\int \frac{1}{t - \frac{1}{2}} d t

e^{- y} sin (x) + y^{^{'}} = 0

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

\int_{- 3}^{2} (6 - x - x^{2}) d x

\frac{d}{d x} (e^{2 s i n^{2} (x)})

What is the derivative of log_{10}(4x) ?
The derivative of log_{10}(4x) is 1/(ln(10)x)
What is the first derivative of log_{10}(4x) ?
The first derivative of log_{10}(4x) is 1/(ln(10)x)