What is the derivative of ln|x-1|-ln|x-3| ?

The derivative of ln|x-1|-ln|x-3| is -2/((x-1)(x-3))

What is the first derivative of ln|x-1|-ln|x-3| ?

The first derivative of ln|x-1|-ln|x-3| is -2/((x-1)(x-3))

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

- \frac{2}{( x - 1 ) ( x - 3 )}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{1}{x - 1} - \frac{1}{x - 3}

Simplify

\frac{1}{x - 1} - \frac{1}{x - 3} : - \frac{2}{( x - 1 ) ( x - 3 )}

= - \frac{2}{( x - 1 ) ( x - 3 )}

\int arccsc (\frac{t}{2}) d t

x \to 2 lim (x^{2})

(7 a + 1)^{2}

x \to 9 lim (\frac{4}{x - 9})

\int_{0}^{2} \frac{5 x - 15}{2 x - 3} d x

What is the derivative of ln|x-1|-ln|x-3| ?
The derivative of ln|x-1|-ln|x-3| is -2/((x-1)(x-3))
What is the first derivative of ln|x-1|-ln|x-3| ?
The first derivative of ln|x-1|-ln|x-3| is -2/((x-1)(x-3))