Differentiate P(t) = cos⁴(t) + cos(t⁴)

JAMB Mathematics 2024 103 views

Differentiate P(t) = cos⁴(t) + cos(t⁴)

  1. dP(t)/dt = -4(sin(t)cos³(t) – t³sin(t⁴))
  2. dP(t)/dt = -4(sin(t⁴)cos³(t) + t³sin(t))
  3. dP(t)/dt = -4(sin³(t)cos(t) + t³sin(t⁴))
  4. dP(t)/dt = -4(sin(t)cos³(t) + t³sin(t⁴)) ✓

Explanation

Prevention is better than cure. Primary prevention: stop disease occurring (vaccination, hygiene, sanitation). Secondary prevention: early detection and treatment (screening, check-ups). Tertiary prevention: reduce complications of existing disease.

Vaccination stimulates immunity without causing disease. Herd immunity: if enough are immune, disease cannot spread easily. Hygiene: handwashing prevents many infections. Sanitation: clean water and waste disposal essential.

Public health measures: health education, environmental control (mosquito control for malaria), food safety regulation, disease surveillance. Prevention is more cost-effective than treatment.

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