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Popular >

derivative of f(x)=(x-1)*ln(x-1)

Solution

derivative of

f (x) = (x - 1) \cdot 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

derivative of-e^{x-1}

\frac{d}{d x} (- e^{x - 1})

integral of (ln(x)-1)/(ln^2(x))

\int \frac{ln ( x ) - 1}{ln ^{2} ( x )} d x

derivative of e^{(2x/2})

\frac{d}{d x} (e^{\frac{2 x}{2}})

integral of (cos(2x))/2

\int \frac{cos ( 2 x )}{2} d x

limit as x approaches-2 of (x^2+6)/(x+2)

x \to - 2 lim (\frac{x ^{2} + 6}{x + 2})

Frequently Asked Questions (FAQ)

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