What is the derivative of log_{3}(3x-7) ?

The derivative of log_{3}(3x-7) is 3/(ln(3)(3x-7))

What is the first derivative of log_{3}(3x-7) ?

The first derivative of log_{3}(3x-7) is 3/(ln(3)(3x-7))

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\frac{d}{d x} (lo g_{3} (3 x - 7))

\frac{3}{ln ( 3 ) ( 3 x - 7 )}

Solution steps

\frac{d}{d x} (lo g_{3} (3 x - 7))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 3 x - 7 )}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (3 x - 7))

Apply the chain rule:

\frac{1}{3 x - 7} \frac{d}{d x} (3 x - 7)

= \frac{1}{3 x - 7} \frac{d}{d x} (3 x - 7)

\frac{d}{d x} (3 x - 7) = 3

= \frac{1}{ln ( 3 )} \cdot \frac{1}{3 x - 7} \cdot 3

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{3 x - 7} \cdot 3 : \frac{3}{ln ( 3 ) ( 3 x - 7 )}

= \frac{3}{ln ( 3 ) ( 3 x - 7 )}

What is the derivative of log_{3}(3x-7) ?
The derivative of log_{3}(3x-7) is 3/(ln(3)(3x-7))
What is the first derivative of log_{3}(3x-7) ?
The first derivative of log_{3}(3x-7) is 3/(ln(3)(3x-7))