Cumulative Vocab

  1. power rule
    multiply original by exponent (if constant), then reduce exponent by 1
  2. chain rule
    take the derivative of the outside function times the derivative of the inside function
  3. product rule
    deriv the first times second plus first times deriv second
  4. quotient rule
    deriv first times second minus first deriv second divided by second squared
  5. differentiability
    implies continuity
  6. indefinite integral
    g(x)=integral f(x)dx <=> g'(x)=f'(x)
  7. power rule (integral)
    increase exponent by 1, then divide by new exponent and add C
  8. natural exponential integral
    eu + C
  9. base-b exponential
    to differentiate, multiply by ln b and to integrate, divide by ln b (plus C)
  10. mean value theorem
    • f different (a,b)
    • f cont [a,b] => at least one number c such that f'(c)=f(b) - f(a)/b-a
  11. fundamental theorem of calculus
    f integral and g(x)= integral f(x)dx=>intrgral a to b f(x)dx=g(b)-g(a)
  12. fundamental theorem derivative form
    g(x)=integral from a to c f(t)dt=> g'(x)=f(x)
  13. natural log function
    the derivative is the reciprocal function
Card Set
Cumulative Vocab
AP Calculus