Question

Find the derivative of e^(tan-1(x))

Answer 1

`\displaystyle (dy)/(dx) = (e^(\arctan x))/(x^2 + 1)`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Rule [Chain Rule]:
`\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

Explanation:

Step 1: Define

Identify

`\displaystyle y = e^(\arctan x)`

Step 2: Differentiate

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

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

Unit: Differentiation