Answer:
\(\displaystyle \frac{dy}{dx} = 6x + 79x^{78}\)
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
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:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle y = 3x^2 + x^{79}\)
Step 2: Differentiate
- Derivative Property [Addition/Subtraction]: \(\displaystyle y' = \frac{d}{dx}[3x^2] + \frac{d}{dx}[x^{79}]\)
- Rewrite [Derivative Property - Multiplied Constant]: \(\displaystyle y' = 3\frac{d}{dx}[x^2] + \frac{d}{dx}[x^{79}]\)
- Basic Power Rule: \(\displaystyle y' = 6x + 79x^{78}\)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
