What is the derivative of log_{3}(4x-3) ?

The derivative of log_{3}(4x-3) is 4/(ln(3)(4x-3))

What is the first derivative of log_{3}(4x-3) ?

The first derivative of log_{3}(4x-3) is 4/(ln(3)(4x-3))

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\frac{d}{d x} (lo g_{3} (4 x - 3))

\frac{4}{ln ( 3 ) ( 4 x - 3 )}

Solution steps

\frac{d}{d x} (lo g_{3} (4 x - 3))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 4 x - 3 )}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (4 x - 3))

Apply the chain rule:

\frac{1}{4 x - 3} \frac{d}{d x} (4 x - 3)

= \frac{1}{4 x - 3} \frac{d}{d x} (4 x - 3)

\frac{d}{d x} (4 x - 3) = 4

= \frac{1}{ln ( 3 )} \cdot \frac{1}{4 x - 3} \cdot 4

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{4 x - 3} \cdot 4 : \frac{4}{ln ( 3 ) ( 4 x - 3 )}

= \frac{4}{ln ( 3 ) ( 4 x - 3 )}

\int cot^{3} (\frac{x}{2}) csc^{4} (\frac{x}{2}) d x

f (x) = 5 e^{x}, at x = 4

\int (sin (2 x))^{3} d x

\int (\frac{1}{x ^{3} + 1}) d x

x (2 x + 1)^{3}

What is the derivative of log_{3}(4x-3) ?
The derivative of log_{3}(4x-3) is 4/(ln(3)(4x-3))
What is the first derivative of log_{3}(4x-3) ?
The first derivative of log_{3}(4x-3) is 4/(ln(3)(4x-3))