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

The derivative of ln(x)*x is 1+ln(x)

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

The first derivative of ln(x)*x is 1+ln(x)

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derivative of

ln (x) \cdot x

1 + ln (x)

Solution steps

\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

= \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

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

Simplify

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

= 1 + ln (x)

\frac{\partial}{\partial u} (4 sin (u) cos (v))

x \to 0 + lim (tan (2 x))

(8 x + 9)^{- 2}

\frac{d}{d x} (x^{3} - 12 x)

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