Derivative of ln(2x)

\frac{d}{dx}\left[\ln\left(2 x\right)\right] = \frac{1}{x}.

\frac{d}{dx}\left[\ln\left(2 x\right)\right] = \frac{1}{x}

Surprisingly, the same as the derivative of ln x. ln(2x) = ln 2 + ln x, and the constant ln 2 disappears when you differentiate.

Constant multiple rule
Pull the constant factor out front.
$\frac{d}{dx}\left[2 x\right] = 2 \cdot \frac{d}{dx}\left[x\right]$
Logarithm rule + chain rule
Outer function $\ln\left(□\right)$ , inner u = $2 x$ ; multiply the outer derivative by u′.
$\frac{d}{dx}\left[\ln\left(2 x\right)\right] = \frac{1}{2 x} \cdot \frac{d}{dx}\left[2 x\right]$

Drag the graph · at x = 3.27 the slope is 0.30581, the height of the dashed curve.

Questions students ask

What is the derivative of ln(2x)?

$\frac{d}{dx}\left[\ln\left(2 x\right)\right] = \frac{1}{x}$ .

How do you find the derivative of ln(2x)?

Surprisingly, the same as the derivative of ln x. ln(2x) = ln 2 + ln x, and the constant ln 2 disappears when you differentiate.

What is the integral of ln(2x)?

Use the integral calculator to find the antiderivative of ln(2x) step by step.