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^{n1}

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'


when factoring (3x^{2}2x)^{4}
 (3x^{2}2x)^{4}
 =[x(3x2)]^{4}
=x
^{4}(3x2)
^{4}

quotient rule
 if u(x) and v(x) are differentiable then

what should you always do before trying to solve for a derivative?