What is the derivative of (ln(x)dx) ?

The derivative of (ln(x)dx) is d(1+ln(x))

What is the first derivative of (ln(x)dx) ?

The first derivative of (ln(x)dx) is d(1+ln(x))

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

d (1 + ln (x))

Solution steps

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

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = ln (x), g = x

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

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

\frac{d x}{d x} = 1

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

Simplify

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

= d (1 + ln (x))

x \to - 1 + lim (2 x + 2)

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What is the derivative of (ln(x)dx) ?
The derivative of (ln(x)dx) is d(1+ln(x))
What is the first derivative of (ln(x)dx) ?
The first derivative of (ln(x)dx) is d(1+ln(x))