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derivatives 1
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what is the derivative of f(x) defined as?
derivative of f(x) is
provided the limit exists
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
derivative is also what?
a function
* provided the limit exists
when is function f(x) called differentiable?
at x=a if limit f'(a) exists
differentiable
everywhere
if f'(x) exists for all x
what is the process of taking a derivative called?
differentiation
when is f(x) not differentiable?
if f'(a) or f'(x) D.N.E. at x=a or all x values
what is diff b/twn f'(a) and f'(x)
f'(a) = number
f'(x) = function
write prime notation, liebniz notation
f'(x)
how to find derivative of f(x) = x
^{2 }
+ 3 with limits?
sub it into equation, use lim approaching h
constant function rule
if f(x) = k
f'(x) = 0
includes values like pi, and other numbers
power rule
if f(x) = x
^{n}
^{}
f'(x) = nx
^{n-1}
constant multiple rule
if f(x) = kg(x), where k is set real numbers and g(x) differentiable
f'(x) = kg'(x)
proof for constant multiple rule
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'
power of a function rule
when factoring (3x
^{2}
-2x)
^{4}
(3x
^{2}
-2x)
^{4}
=[x(3x-2)]
^{4}
=x
^{4}
(3x-2)
^{4}
quotient rule
if u(x) and v(x) are differentiable then
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
2012-10-14T02:58:27Z
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