Calculus • Step-by-Step

Derivative of e^(2x) with Steps

Find the derivative of e^(2x) step by step using the Chain Rule. Shows inner function substitution to get 2e^(2x).

Problem Statement

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

Final Result

f'(x) = 2 \cdot e^{2 \cdot x}

Formula Required: Chain Rule for Exponentials

Differentiate the outside exponential function, then multiply by the derivative of the inside exponent.

\frac{d}{dx}[e^{u}] = e^u \cdot \frac{du}{dx}

2 Steps

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

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

Apply the Chain Rule to compute the derivative.

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

Interactive Calculator

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

The outside function is e^u and inside is u = 2x. Since du/dx = 2, multiplying gives e^(2x) · 2 = 2e^(2x).