3.3 Techniques of Differentation

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Presentation transcript:

3.3 Techniques of Differentation Rita Korsunsky

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

proof proof

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

proof

proof proof

Product Rule proof

Quotient Rule proof

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

Power Rule: proof By Reciprocal rule:

Example #1

Example #2 SOLUTION Simplify y: Find the slope:

Example #3

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

Example #5