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