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Popular >

derivative of (x-1ln|x-1|)

Solution

\frac{d}{d x} ((x - 1) ln ∣ x - 1 ∣)

Solution

ln ∣ x - 1 ∣ + 1

Solution steps

\frac{d}{d x} ((x - 1) ln ∣ x - 1 ∣)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 1, g = ln ∣ x - 1 ∣

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

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

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

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

Simplify

1 \cdot ln ∣ x - 1 ∣ + \frac{1}{x - 1} (x - 1) : ln ∣ x - 1 ∣ + 1

= ln ∣ x - 1 ∣ + 1

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Frequently Asked Questions (FAQ)

What is the derivative of (x-1ln|x-1|) ?
The derivative of (x-1ln|x-1|) is ln|x-1|+1
What is the first derivative of (x-1ln|x-1|) ?
The first derivative of (x-1ln|x-1|) is ln|x-1|+1