Presentation on theme: "Key Ideas about Derivatives (3/20/09)"— Presentation transcript:
1 Key Ideas about Derivatives (3/20/09) The definition and meaning:f ‘ (x) = lim h -> 0 (f (x+h ) – f (x)) / hf ‘ (x) is the instantaneous rate of change of the function f at the point (x, f (x)). If f is graphed, f ‘ is the slope of the tangent line to the graph at that point.
2 The RulesThe Rules tell us how to take the derivative of combinations of functions.Constant Multiplier RuleSum and Difference RuleProduct RuleQuotient RuleChain Rule
3 The FactsThe Facts tell us how to take the derivative for different classes of common functions.d/dx ( x r ) = r x r – 1 (r any constant)d/dx ( a x ) = a x ln(a) (a constant > 0)In particular, d/dx ( e x ) = e xd/dx ( loga (x ) = 1 / (x ln(a))In particular, d/dx ( ln (x) ) = 1 / x