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