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Popular >

derivative of 3xln(2x)

Solution

\frac{d}{d x} (3 x ln (2 x))

Solution

3 (ln (2 x) + 1)

Solution steps

\frac{d}{d x} (3 x ln (2 x))

Take the constant out:

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

= 3 \frac{d}{d x} (x ln (2 x))

Apply the Product Rule:

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

f = x, g = ln (2 x)

= 3 (\frac{d x}{d x} ln (2 x) + \frac{d}{d x} (ln (2 x)) x)

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

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= 3 (1 \cdot ln (2 x) + \frac{1}{x} x)

Simplify

3 (1 \cdot ln (2 x) + \frac{1}{x} x) : 3 (ln (2 x) + 1)

= 3 (ln (2 x) + 1)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 3xln(2x) ?
The derivative of 3xln(2x) is 3(ln(2x)+1)
What is the first derivative of 3xln(2x) ?
The first derivative of 3xln(2x) is 3(ln(2x)+1)