Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{e^{\arctan x}}{x^2 + 1}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
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 y = e^{\arctan x}[/tex]
Step 2: Differentiate
- Exponential Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = e^{\arctan x}(\arctan x)'[/tex]
- Trigonometric Differentiation: [tex]\displaystyle y' = \frac{e^{\arctan x}}{x^2 + 1}[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
