What is the derivative of 3xln(x/2) ?

The derivative of 3xln(x/2) is 3(ln(x/2)+1)

What is the first derivative of 3xln(x/2) ?

The first derivative of 3xln(x/2) is 3(ln(x/2)+1)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = ln (\frac{x}{2})

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

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

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

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

Simplify

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

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

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sin (4 t + \frac{π}{3})

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\int \frac{1}{3 x ^{2} - 12 x + 15} d x

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