 Generalized Power Derivative  Derivative of Sums  Product Rule/Chain Rule  Quotient Rule

 Generalized Power Derivative ~ n[ ax^(n-1) where a=coefficient and n= a number  Examples:  1) x² = 2x  2) 4x³ = 12x²  3) 6x = 6 ( imagine that x is raised to the first power )  4) (2x²-3x)³ = 3(2x²-3x)²(4x-3)

 Derivative of Sums~ f’(x) + g’(x)  Examples:  1) 5xˆ9 – (3/x²) = 45xˆ8 + (6/x³)  2) {3x² + x – 2}/ x² = xˆ(-2)[3x² + x -2] = 3 + xˆ(-1) -2xˆ(-2) = (-1/x²) + (4/x³)

 Product Rule/Chain Rule~ (f’(x) g(x)) + (f(x) g’(x))  Examples:  1) (x²)(x³) = 2x(x³) + (x²)3x = 2xˆ4 + 3x³

 Quotient Rule~ {(f'(x) g(x)) - (f(x) g'(x) )} /{g (x)} 2  Examples:  1) x³/ (x² + 7x) = [3x²(x²+7x) – x³(2x+7)] / (x²+7x)²

 The limit is described as the behavior of a function as it gets closer to a certain point.  LIM f(x) = L x→c  Where “L” is a real number and “c” is what the limit is going to.

 For some functions solving for the limit is as simple as plugging “c” into the function.  Example: LIM f(x) 3x-9 = 3 x→4  LIM f(x) x² + 2x -1/ (x+1) = 1 X→1

 It may also help to look at the graph of the function to find the limit.  Example: LIM f(x) 1/x = 0 x→∞

 There are many different ways to find derivatives and to find limits.  This was just an introduction.  You should have learned some of the basics of finding both limits and derivatives.