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Calculus Derivatives and Rules Summary

Understand derivatives and rules in calculus including derivative facts and established rules for differentiation. Practice exercises to reinforce learning.

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Calculus Derivatives and Rules Summary

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  1. Clicker Question 1 • What is the derivative of f (x ) = 2xsin(x ) ? • A. 2xcos(x ) • B. 2xln(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 ))

  2. 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

  3. Established (for now) Derivative Facts (12/1/10) • d/dx (xr ) = rxr -1 provided r is a whole number (positive or negative). • d/dx (ax ) = ax 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)

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

  5. Assignment for Friday • Do Exercises 3, 7, 11, 17, 21 and 22 on page 195. • Hand-in #4 is due Thursday (12/2) at 4:45.

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