Question

Finding Higher-Order Derivatives In Exercise, find the second derivative of the function.

f(x) = 5x

Answer 1

f''(x) = 0

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:
`\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)`

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Identify

f(x) = 5x

Step 2: Differentiate

1. Basic Power Rule [Derivative Property - Multiplied Constant]: f'(x) = 5x¹⁻¹
2. Simplify: f'(x) = 5
3. Basic Power Rule [Derivative of a Constant]: f''(x) = 0

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

Unit: Differentiation