Find the derivative of the function.
3
f(x) = 4x + 20x4
f'(x)=
1 answer:
Answer:
f'(x) = 4 + 80x³
General Formulas and Concepts:
<u>Calculus</u>
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
Step-by-step explanation:
<u>Step 1: Define function</u>
f(x) = 4x + 20x⁴
<u>Step 2: Find 1st derivative</u>
- 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
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