# derivatives 1

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 Author: kayekitty ID: 177471 Filename: derivatives 1 Updated: 2012-10-13 22:58:27 Tags: calculus derivatives Folders: Description: calculus derivatives 1 Show Answers:

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1. what is the derivative of f(x) defined as?
• derivative of f(x) is
• 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)
9. how to find derivative of f(x) = x+ 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
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
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
18. what should you always do before trying to solve for a derivative?
• SIMPLIFY
• ACA

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