Clicker Question 1 What is the derivative of f (x ) = 2x sin(x ) ?

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Presentation transcript:

Clicker Question 1 What is the derivative of f (x ) = 2x sin(x ) ? A. 2x cos(x ) B. 2x ln(2) cos(x ) C. 2x (ln(2) cos(x ) + sin(x )) D. 2x (cos(x ) + sin(x )) E. 2x (ln(2) sin(x ) + cos(x ))

Clicker Question 2 What is the instantaneous rate of change of g (x ) = 3 tan(x ) at x = /3 ? A. 3 B. 3 sec2(x ) C. 12 D. 4 E. 6

Established (for now) Derivative Facts (11/30/11) d/dx (x r ) = r x r - 1 provided r is a whole number (positive or negative). d/dx (a x ) = a x ln(a) d/dx ( sin(x )) = cos(x ) d/dx (cos(x )) = -sin(x ) <- similar to proof for the sin d/dx (tan(x )) = sec2(x ) d/dx (sec(x )) = sec(x )tan(x) d/dx (cot(x )) = ? <- homework problem d/dx (csc(x )) = -csc(x )cot(x)

Established (for now) Derivative Rules Constant Multiplier Rule Sum and Difference Rule Product Rule Quotient Rule One more to go: Chain Rule

Assignment for Friday Do Exercises 3, 7, 11, 17, 22 and 34 on page 197. Hand-in #4 is due Thursday (12/1) at 4:45.