What is the derivative of ln|4x-3| ?

The derivative of ln|4x-3| is 4/(4x-3)

What is the first derivative of ln|4x-3| ?

The first derivative of ln|4x-3| is 4/(4x-3)

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\frac{d}{d x} (ln ∣ 4 x - 3 ∣)

\frac{4}{4 x - 3}

Solution steps

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

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

Simplify

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

= \frac{4}{4 x - 3}

\int x (2 x - 1) d x

x \to π lim (ln ∣ cos (x) - 8 ∣)

\int e^{- k x} d x

\frac{d}{d t} (e^{t})

x \to \infty lim (3 x - 5)

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