Respuesta :

Space

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

Step-by-step 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

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