Question

Derivative of 3x^2 + x^79

Answer 1

`\displaystyle (dy)/(dx) = 6x + 79x^(78)`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:

Derivative Property [Addition/Subtraction]:
`\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]`

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Identify

`\displaystyle y = 3x^2 + x^(79)`

Step 2: Differentiate

1. Derivative Property [Addition/Subtraction]:
   `\displaystyle y' = (d)/(dx)[3x^2] + (d)/(dx)[x^(79)]`
2. Rewrite [Derivative Property - Multiplied Constant]:
   `\displaystyle y' = 3(d)/(dx)[x^2] + (d)/(dx)[x^(79)]`
3. Basic Power Rule:
   `\displaystyle y' = 6x + 79x^(78)`

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

Unit: Differentiation