Question

Find the derivative of the function.
3
f(x) = 4x + 20x4
f'(x)=

Answer 1

f'(x) = 4 + 80x³

General Formulas and Concepts:

Calculus

The definition of a derivative is the slope of the tangent line.

We can take the derivative/distribute it over addition and subtraction.

Basic Power Rule:

• f(x) = cxⁿ
• f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define function

f(x) = 4x + 20x⁴

Step 2: Find 1st derivative

1. Basic Power Rule (1st term): f'(x) = 4 · 1x¹⁻¹ + 20x⁴
2. Basic Power Rule (2nd term): f'(x) = 4 · 1x¹⁻¹ + 20 · 4x⁴⁻¹
3. Simplify: f'(x) = 4 + 80x³