Question

What is the derivative of 5x^4+4?

Answer 1

`\displaystyle (dy)/(dx) = 20x^3`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:
`\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)`

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 = 5x^4 + 4`

Step 2: Differentiate

1. Derivative Property [Addition/Subtraction]:
   `\displaystyle y' = (d)/(dx)[5x^4] + (d)/(dx)[4]`
2. Rewrite [Derivative Property - Multiplied Constant]:
   `\displaystyle y' = 5(d)/(dx)[x^4] + (d)/(dx)[4]`
3. Basic Power Rule:
   `\displaystyle y' = 20x^3`

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

Unit: Differentiation