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