What is the derivative of log_{3}(5x-1) ?

The derivative of log_{3}(5x-1) is 5/(ln(3)(5x-1))

What is the first derivative of log_{3}(5x-1) ?

The first derivative of log_{3}(5x-1) is 5/(ln(3)(5x-1))

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\frac{d}{d x} (lo g_{3} (5 x - 1))

\frac{5}{ln ( 3 ) ( 5 x - 1 )}

Solution steps

\frac{d}{d x} (lo g_{3} (5 x - 1))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 5 x - 1 )}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (5 x - 1))

Apply the chain rule:

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

= \frac{1}{5 x - 1} \frac{d}{d x} (5 x - 1)

\frac{d}{d x} (5 x - 1) = 5

= \frac{1}{ln ( 3 )} \cdot \frac{1}{5 x - 1} \cdot 5

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{5 x - 1} \cdot 5 : \frac{5}{ln ( 3 ) ( 5 x - 1 )}

= \frac{5}{ln ( 3 ) ( 5 x - 1 )}

y = \frac{5}{x}, (4, \frac{5}{4})

t^{2} \cdot t^{3} + 2

\frac{1}{2 r} + \frac{1}{9 r ^{\frac{8}{9}}}

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

n = 1 \sum \infty \frac{4}{n ^{2} + 1}

What is the derivative of log_{3}(5x-1) ?
The derivative of log_{3}(5x-1) is 5/(ln(3)(5x-1))
What is the first derivative of log_{3}(5x-1) ?
The first derivative of log_{3}(5x-1) is 5/(ln(3)(5x-1))