Home > Flashcards > Print Preview
The flashcards below were created by user
kayekitty
on FreezingBlue Flashcards. What would you like to do?

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?

