Derivative of $e^{x}$

The derivative of $e^{x}$ is $e^{x}$ .

f(x) =

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

Type any function of x; the derivative is computed symbolically in your browser.

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

Graph of f(x) = exp(x) and its derivative. The dashed line is the tangent at x = 1; its slope is f'(1) = 2.7183.

How to work it out

1
We differentiate $f(x) = e^{x}$ with respect to x. The rule that applies is the standard derivative.
$f(x) = e^{x}$
2
This is a standard derivative from the table.
3
Simplify:
$f'(x) = e^{x}$
4
Differentiating once more gives the second derivative, which tells you about curvature:
$f''(x) = e^{x}$

LaTeX source of the formulas on this page

\[ \frac{d}{dx}\left[e^{x}\right] = e^{x} \]
\[ f(x) = e^{x} \]
\[ f'(x) = e^{x} \]
\[ f''(x) = e^{x} \]

What is the derivative of exp(x)?

The derivative of $e^{x}$ is $e^{x}$ .

What is the second derivative of exp(x)?

exp(x).

Which rule do you use for exp(x)?

The standard derivative.

What is the slope of exp(x) at x = 1?

2.7182818.