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

User Manukall
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Answer:


\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

User Billmalarky
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