Derivative of `e^(x)`

Step-by-step differentiation

Answer

\frac{d}{d x} [e^{x}]

e^{x}

Step-by-step solution

1Derivative of eˣ
$\frac{d}{d x} [e^{x}] = e^{x}$
$e^{x}$ is its own derivative — a unique property of the natural exponential.
✓Final Answer
$\frac{d}{d x} [e^{x}] = e^{x}$
The first derivative simplifies to $e^{x}$ .

Understanding this derivative

Differentiating e^(x) is a single-rule problem: everything follows from the exponential rule. That makes it a good expression for isolating and practicing that one technique.

The exponential function eˣ is its own derivative — the only function (up to constant multiples) with that property — which is why it appears unchanged in the result.

A good way to verify a derivative by hand is to compare it against the step-by-step breakdown above — each step names the rule being applied, so you can pinpoint exactly where your own work diverges if the answers differ.

Learn the rules used here

Derivatives of Transcendental Functions

Try a different expression

Open Calculator

Derivative of e^(x)

Step-by-step solution

Understanding this derivative

Learn the rules used here

Derivative of `e^(x)`