Calculus • Step-by-Step

Derivative of eˣ with Steps

Differentiate eˣ with complete explanations. Explains why the natural exponential function e^x is its own derivative.

Problem Statement

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

Final Result

f'(x) = e^{x}

Formula Required: Exponential Derivative Rule

Euler's number e is uniquely defined such that the slope of e^x at any point equals the function value itself.

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

2 Steps

Set up the differentiation problem with respect to variable $x$.

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

Apply the Exponential Rule to compute the derivative.

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

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

By definition of the base e, lim(h→0) (e^h - 1)/h = 1. Applying the limit definition gives d/dx[e^x] = e^x · 1 = e^x.