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derivatives 1

  1. what is the derivative of f(x) defined as?
    • derivative of f(x) is
    • Image Upload 2
    • provided the limit exists
  2. what are the two interpretations o derivative?
    • 1. slope o tangent line o function at that point
    • 2. instantaneous rate o change o function at the point
  3. derivative is also what?
    • a function
    • * provided the limit exists
  4. when is function f(x) called differentiable?
    • at x=a if limit f'(a) exists
    • differentiable everywhere if f'(x) exists for all x
  5. what is the process of taking a derivative called?
    differentiation
  6. when is f(x) not differentiable?
    if f'(a) or f'(x) D.N.E. at x=a or all x values
  7. what is diff b/twn f'(a) and f'(x)
    • f'(a) = number
    • f'(x) = function
  8. write prime notation, liebniz notation
    • f'(x)
    • Image Upload 4
  9. how to find derivative of f(x) = x2 + 3 with limits?
    sub it into equation, use lim approaching h 
  10. constant function rule
    • if f(x) = k
    • f'(x) = 0
    • includes values like pi, and other numbers
  11. power rule
    • if f(x) = xn
    • f'(x) = nxn-1
  12. constant multiple rule
    • if f(x) = kg(x), where k is set real numbers and g(x) differentiable
    • f'(x) = kg'(x)
  13. proof for constant multiple rule
    Image Upload 6
  14. product rule
    • let u(x) and v(x) be differentiable
    • (uv)'=u'v + uv'
    • if u(x) and v(x)  and h(x) be differentiable
    • (uvh)'=u'vh + uv'h + uvh'
  15. power of a function rule
    Image Upload 8
  16. when factoring (3x2-2x)4
    • (3x2-2x)4
    • =[x(3x-2)]4

    =x4(3x-2)4
  17. quotient rule
    • if u(x) and v(x) are differentiable then
    • Image Upload 10
  18. what should you always do before trying to solve for a derivative?
    • SIMPLIFY
    • ACA
Author
kayekitty
ID
177471
Card Set
derivatives 1
Description
calculus derivatives 1
Updated

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