derivatives Flashcards
definition of the derivative

power rule

derivative of exponential function (including simple case)

derivative of logarithmic function

derivative of sin(ax)

derivative of cos (ax)

derivative of tan(ax)

derivative of csc(ax)

derivative of sec(ax)

derivative of cot(ax)

derivative of arcsin(ax)

derivative of arccos(ax)

derivative of arctan(ax)

derivative of [f(x)g(x)]

critical point definition
critical point = a point (c) in the domain of f at which
f’(c) = 0, or
f’(c) is undefined
significance of the sign of f’(x)
if f’(x) > 0 (positive), the function is increasing on the given interval
if f’(x) < 0 (negative), the function is decreasing on the given interval
inflection point (definition)
inflection point = a point on the graph where it changes from concave up to concave down
relationship btwn inflection points and critical points
all inflection points are critical points, but not all critical points are inflection points
significance of the sign of f’‘(x)
if f’‘(x) > 0 (positive), the function is concave up on the given interval
if f’‘(x) < 0 (negative), the function is concave down on the given interval
chain rule

product rule

quotient rule

algorithm for implicit differentiation

algorithm for logarithmic differentiation

l’Hopital’s rule

indeterminate forms that can’t be solved using l’hopital (product, difference, exponential)
