What is the derivative of log_{10}(3x+2016) ?

The derivative of log_{10}(3x+2016) is 1/(ln(10)(x+672))

What is the first derivative of log_{10}(3x+2016) ?

The first derivative of log_{10}(3x+2016) is 1/(ln(10)(x+672))

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derivative of

lo g_{10} (3 x + 2016)

\frac{1}{ln ( 10 ) ( x + 672 )}

Solution steps

\frac{d}{d x} (lo g_{10} (3 x + 2016))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 3 x + 2016 )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (3 x + 2016))

Apply the chain rule:

\frac{1}{3 x + 2016} \frac{d}{d x} (3 x + 2016)

= \frac{1}{3 x + 2016} \frac{d}{d x} (3 x + 2016)

\frac{d}{d x} (3 x + 2016) = 3

= \frac{1}{ln ( 10 )} \cdot \frac{1}{3 x + 2016} \cdot 3

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{3 x + 2016} \cdot 3 : \frac{1}{ln ( 10 ) ( x + 672 )}

= \frac{1}{ln ( 10 ) ( x + 672 )}

\frac{d}{d t} (10 t)

\frac{d}{d a} (4 a)

sin^{3} (1 - 2 x)

e^{2} t

ln (x^{2} + x)

What is the derivative of log_{10}(3x+2016) ?
The derivative of log_{10}(3x+2016) is 1/(ln(10)(x+672))
What is the first derivative of log_{10}(3x+2016) ?
The first derivative of log_{10}(3x+2016) is 1/(ln(10)(x+672))