What is the derivative of xln(3x) ?

The derivative of xln(3x) is ln(3x)+1

What is the first derivative of xln(3x) ?

The first derivative of xln(3x) is ln(3x)+1

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\frac{d}{d x} (x ln (3 x))

ln (3 x) + 1

Solution steps

\frac{d}{d x} (x ln (3 x))

Apply the Product Rule:

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

f = x, g = ln (3 x)

= \frac{d x}{d x} ln (3 x) + \frac{d}{d x} (ln (3 x)) x

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= 1 \cdot ln (3 x) + \frac{1}{x} x

Simplify

1 \cdot ln (3 x) + \frac{1}{x} x : ln (3 x) + 1

= ln (3 x) + 1

What is the derivative of xln(3x) ?
The derivative of xln(3x) is ln(3x)+1
What is the first derivative of xln(3x) ?
The first derivative of xln(3x) is ln(3x)+1