# What is the derivative of 2 ln x?

#### Understand the Problem

The question is asking for the derivative of the function 2 ln(x), which involves applying differentiation rules to find the rate of change of the function with respect to x.

$$\frac{2}{x}$$

The final answer is ( \frac{2}{x} )

#### Steps to Solve

1. Identify the function to differentiate

The given function is $f(x) = 2 \ln(x)$.

1. Apply the constant multiple rule

The constant multiple rule in differentiation states that the derivative of a constant times a function is the constant times the derivative of the function: [ \frac{d}{dx} [c \cdot f(x)] = c \cdot \frac{d}{dx} [f(x)] ] Here, $c = 2$ and $f(x) = \ln(x)$.

1. Differentiate the natural logarithm function

Recall that the derivative of $\ln(x)$ with respect to $x$ is $\frac{1}{x}$: [ \frac{d}{dx} [\ln(x)] = \frac{1}{x} ]

1. Combine the results

Multiply the constant $2$ by the derivative of $\ln(x)$: [ \frac{d}{dx} [2 \ln(x)] = 2 \cdot \frac{1}{x} = \frac{2}{x} ]

The final answer is ( \frac{2}{x} )