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

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

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}

x \to 2 lim (x^{3} - 4)

a sin (\frac{( π \cdot x )}{b})

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

\int \frac{x ^{2} - a ^{2}}{x ^{2}} d x

\int \frac{1}{2} cos (x) d x

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