Question

What is the derivative of 3x+5x

Answer 1

`\displaystyle (d)/(dx)[3x + 5x] = 8`

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

`\displaystyle y = 3x + 5x`

Step 2: Differentiate

1. Simplify:
   `\displaystyle y = 8x`
2. Derivative Property [Multiplied Constant]:
   `\displaystyle y' = 8(d)/(dx)[x]`
3. Basic Power Rule:
   `\displaystyle y' = 8`

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

Unit: Differentiation