Mathematics

There are only six major laws of exponents that determine all that can be done with exponents and exponential functions:

1. a a ax+y x y= (1.39)

2. a a a

= (1.40)

3. (a ) ax y xy= (1.41)

4. (ab) a bx x x= (1.42)

5. a ax/y xy= (1.43)

6. a° = 1 (1.44)

(a b) a 2ab b2 2 2± = ± +

(1.45)

(a b) a 3a b 3ab b3 3 2 2 3± = ± + ±

(1.46)

(a b ) (a b)(a b)2 2− = − +

(1.47)

(a b ) (a b)(a ab b )3 3 2 2± = ± − + +/

(1.48)

(a b) a na b n(n 1)

2! a bn n n 1 n 2 2+ = + +

−

(1.49)

From Figure 1.3, it is seen that the derivative of y = f(x) is continuous and no point of inexion exists between A and B.