Question

Find the derivative of f(x) = e^x^2

Answer 1

`\displaystyle f'(x) = 2xe^\big{x^2}`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

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

Explanation:

Step 1: Define

Identify

`\displaystyle f(x) = e^\big{x^2}`

Step 2: Differentiate

1. Exponential Differentiation [Derivative Rule - Chain Rule]:
   `\displaystyle f'(x) = e^\big{x^2}(x^2)'`
2. Basic Power Rule:
   `\displaystyle f'(x) = 2xe^\big{x^2}`

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

Unit: Differentiation