What is the derivative of (x-1)*ln(x-1) ?

The derivative of (x-1)*ln(x-1) is ln(x-1)+1

What is the first derivative of (x-1)*ln(x-1) ?

The first derivative of (x-1)*ln(x-1) is ln(x-1)+1

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derivative of

(x - 1) \cdot ln (x - 1)

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

x \to 0 lim (\frac{x ^{3} + 3 x}{x})

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\int x cos (π) x d x

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