Respuesta :

Space

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

  1. Exponential Differentiation [Derivative Rule - Chain Rule]:                       [tex]\displaystyle y' = e^{\arctan x}(\arctan x)'[/tex]
  2. Trigonometric Differentiation:                                                                       [tex]\displaystyle y' = \frac{e^{\arctan x}}{x^2 + 1}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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