Derivative of eˣ

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

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

eˣ is the one function whose slope at every point equals its own height. That property is really the definition of the number e ≈ 2.71828.

Drag the graph · at x = 1.20 the slope is 3.3201, the height of the dashed curve.

Questions students ask

What is the derivative of eˣ?

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

How do you find the derivative of eˣ?

eˣ is the one function whose slope at every point equals its own height. That property is really the definition of the number e ≈ 2.71828.

What is the integral of eˣ?

See the integral of eˣ page for the antiderivative with steps.