Question

What’s the derivative of x^2 - 3

Answer 1

Answer:

$\displaystyle \frac{dy}{dx} = 2x$

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

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

Derivative Property [Addition/Subtraction]:                                                         $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$  

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = x^2 - 3$

Step 2: Differentiate

1. Derivative Property [Addition/Subtraction]:                                                 $\displaystyle y' = \frac{d}{dx}[x^2] - \frac{d}{dx}[3]$
2. Basic Power Rule:                                                                                         $\displaystyle y' = 2x$

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

Unit: Differentiation