What is the derivative of 6xln(x) ?

The derivative of 6xln(x) is 6(ln(x)+1)

What is the first derivative of 6xln(x) ?

The first derivative of 6xln(x) is 6(ln(x)+1)

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\frac{d}{d x} (6 x ln (x))

6 (ln (x) + 1)

Solution steps

\frac{d}{d x} (6 x ln (x))

Take the constant out:

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

= 6 \frac{d}{d x} (x ln (x))

Apply the Product Rule:

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

f = x, g = ln (x)

= 6 (\frac{d x}{d x} ln (x) + \frac{d}{d x} (ln (x)) x)

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

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

= 6 (1 \cdot ln (x) + \frac{1}{x} x)

Simplify

6 (1 \cdot ln (x) + \frac{1}{x} x) : 6 (ln (x) + 1)

= 6 (ln (x) + 1)

What is the derivative of 6xln(x) ?
The derivative of 6xln(x) is 6(ln(x)+1)
What is the first derivative of 6xln(x) ?
The first derivative of 6xln(x) is 6(ln(x)+1)