Answer:
\(\displaystyle \frac{d}{dx}[e^\big{2x}] = 2e^\big{2x}\)
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]: \(\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)
Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle y = e^\big{2x}\)
Step 2: Differentiate
- Exponential Differentiation [Derivative Rule - Chain Rule]: \(\displaystyle \frac{d}{dx} = e^\big{2x} \cdot \frac{d}{dx}[2x]\)
- Basic Power Rule [Derivative Property - Multiplied Constant]: \(\displaystyle \frac{d}{dx} = e^\big{2x} \cdot 2\)
- Simplify: \(\displaystyle \frac{d}{dx} = 2e^\big{2x}\)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
