Question

What is the derivative of 3x+5x

Answer 1

Answer:

$\displaystyle \frac{d}{dx}[3x + 5x] = 8$

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:                                                           $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = 3x + 5x$

Step 2: Differentiate

1. Simplify:                                                                                                         $\displaystyle y = 8x$
2. Derivative Property [Multiplied Constant]:                                                   $\displaystyle y' = 8\frac{d}{dx}[x]$
3. Basic Power Rule:                                                                                         $\displaystyle y' = 8$

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

Unit: Differentiation