1. 3.3 Techniques of Differentation
Rita Korsunsky

2. f & g denote differentiable functions
f & g denote differentiable functions. c,m, and b are real numbers, and n is a rational number.

3. proof
proof

4. Power Rule:
proof
If n is a positive integer, then we can expand by using the binomial theorem, obtaining
n-2
n-1

5. proof

6. proof
proof

7. Product Rule
proof

8. Quotient Rule
proof

9. Reciprocal rule
proof
To prove, use quotient rule with f(x)=1

10. Power Rule:
proof
By Reciprocal rule:

11. Example #1

12. Example #2
SOLUTION
Simplify y:
Find the slope:

13. Example #3

14. Example #4 (b) Tangent is horizontal : slope = 0, or numerator = 0
Tangent is vertical if the slope DNE, or denominator =0

15. Example #5