Derivative of e²ˣ

\frac{d}{dx}\left[e^{2 x}\right] = 2 e^{2 x}.

\frac{d}{dx}\left[e^{2 x}\right] = 2 e^{2 x}

The chain rule multiplies by the inner derivative 2: every doubling of the rate inside the exponent doubles the slope.

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

Drag the graph · at x = 0.08 the slope is 2.347, the height of the dashed curve.

Questions students ask

What is the derivative of e²ˣ?

$\frac{d}{dx}\left[e^{2 x}\right] = 2 e^{2 x}$ .

How do you find the derivative of e²ˣ?

The chain rule multiplies by the inner derivative 2: every doubling of the rate inside the exponent doubles the slope.

What is the integral of e²ˣ?

Use the integral calculator to find the antiderivative of e²ˣ step by step.