c/c_Calcul infinitésimal_12e_Différentiation : taux de variationrègles de différentiationordre élevé, impliciteapplications (differentiation)

Subject
Calculus
Grade
12 année
Concept/Content
differentiation:
  • rate of change
  • differentiation rules
  • higher order, implicit
  • applications (differentiation)
Elaboration
  • history
  • definition of derivative
  • notation
  • average versus instantaneous
  • slope of secant and tangent lines
  • power, product; quotient and chain
  • transcendental functions: logarithmic, exponential, trigonometric
  • relating graph of f(x) to f'(x) and f''(x)
  • increasing/decreasing, concavity
  • differentiability, mean value theorem
  • Newton’s method
  • problems in contextual situations,  including related rates and optimization problems
keywords
differentiation
rate of change
differentiation rules
applications (differentiation)