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Popular Calculus >

derivative of (x-1ln(x))

Solution

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

Solution

ln (x) + \frac{x - 1}{x}

Solution steps

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

Apply the Product Rule:

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

f = x - 1, g = ln (x)

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

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

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

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

Simplify

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

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

Graph

Popular Examples

roots asin(((pi*x))/b)

roo t s a sin (\frac{( π \cdot x )}{b})

derivative of (64/(x^2+16))

\frac{d}{d x} (\frac{64}{x ^{2} + 16})

limit as y approaches 2 of (y^3-6y^2+12y-8)/(y^4-4y^3+16y-16)

y \to 2 lim (\frac{y ^{3} - 6 y ^{2} + 12 y - 8}{y ^{4} - 4 y ^{3} + 16 y - 16})

derivative of ln(c)

d er i v a t i v e ln (c)

integral of z/(z^2+z-1)

\int \frac{z}{z ^{2} + z - 1} d z

Frequently Asked Questions (FAQ)

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