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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

Popular Examples

integral from 0 to x^2 of t^2

\int_{0}^{x^{2}} t^{2} d t

derivative of y=5x^4-x^2+6 derivative of

y = 5 x^{4} - x^{2} + 6

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\frac{d}{d x} (2 x + 9)

integral of (4x^3+2x^2+1)/(4x^3-x)

\int \frac{4 x ^{3} + 2 x ^{2} + 1}{4 x ^{3} - x} d x

derivative of (x^3+6)e^x derivative of

(x^{3} + 6) e^{x}

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