D ERIVATIVES Review- 6 Differentiation Rules. For a function f(x) the instantaneous rate of change along the function is given by: Which is called the.

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Presentation transcript:

D ERIVATIVES Review- 6 Differentiation Rules

For a function f(x) the instantaneous rate of change along the function is given by: Which is called the derivative of f Definition of the Derivative Notation:

3) find the Derivative of cos x

Trig Derivatives

The Power Rule If n is a rational number, then the function is differential and

4) Find the derivative

The Sum and Difference Rule The derivative of a sum is the sum of the derivatives Proof pg 111

5) Find the derivative

The Product Rule The product of two differentiable functions f and g is itself differentiable. Moreover, the derivative of f  g is the first times the derivative of the second, plus the second times the derivative of the first Proof pg 119 (f  g) '(x) = f(x) g '(x) + g(x) f '(x)

6) Find the derivative

The Quotient Rule The derivative of f  g is given by: The denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all divided by the denominator squared Proof pg 121

7) Find the derivative

The Chain Rule If g(x) is differentiable then Power rule times the derivative of inside Proof pg 131

8) Find the derivative

9) Find the derivative

H OME W ORK Page 158 # odd, 41, 45, 49, and 51, and Worksheet 6-B