Step-by-Step Derivative Calculation
Given Function:
f(x) = -3.5820821453486×10-7x3 + 0.00176655345471687x2 - 1.74899496695824x + 2160.49118089801
Power Rule: If f(x) = axn, then f'(x) = n·ax(n-1)
Term 1: -3.5820821453486×10-7x3
Coefficient = -3.5820821453486×10-7
Exponent = 3
Multiply: (3) × (-3.5820821453486×10-7) = -1.07462464360458×10-6
Reduce power: x3-1 = x2
✅ First derivative term: -1.07462464360458×10-6x2
Term 2: 0.00176655345471687x2
Coefficient = 0.00176655345471687
Exponent = 2
Multiply: (2) × (0.00176655345471687) = 0.00353310690943374
Reduce power: x2-1 = x1 = x
✅ Second derivative term: 0.00353310690943374x
Term 3: -1.74899496695824x
Coefficient = -1.74899496695824
Exponent = 1
Multiply: (1) × (-1.74899496695824) = -1.74899496695824
Reduce power: x1-1 = x0 = 1
✅ Third derivative term: -1.74899496695824
Term 4: 2160.49118089801
Coefficient = 2160.49118089801
Exponent = 0 (constant term)
Multiply: (0) × (2160.49118089801) = 0
✅ Fourth derivative term: 0
Final Answer:
f'(x) = -1.07462464360458×10-6x2 + 0.00353310690943374x - 1.74899496695824