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Published byEdward Phelps Modified over 9 years ago
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Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx (ln(x)) = d/dx (arcsin(x)) = d/dx (arctan(x)) =
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Derivative Rules Constant Multiplier Rule Sum and Difference Rule Product Rule Quotient Rule Chain Rule
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Clicker Question 1 What is the derivative function of f (x ) = 5x sin(3x ) ? A. 5 cos(3x) B. 15 cos(3x) C. 15x cos(3x) + 5 sin(3x) D. 5x cos(3x) + 5 sin(3x) E. -5x cos(3x) + 5 sin(3x)
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Clicker Question 2 What is the exact instantaneous rate of change of the function g (x ) = 2 x at the point x = 3? A. 8 ln(2) B. 6 ln(2) C. 8 D. 12 E. 12 ln(2)
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Clicker Question 3 What is the slope of the tangent line to the curve y = (x 2 + 3) when x = 2 ? A. 1 / (2 7) B. 4 7 C. 2 7 D. 2 / 7 E. 1 / (4 7)
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A Sample Pointing Our Direction This Semester From your MA 108 final exam: Find all the points in the domain of f (x) = x 4 /4 + x 3 – 2x 2 + 7 at which the tangent line is horizontal. These points are critical. We shall talk about why they are important this semester, along with various other ideas.
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Assignment for Wednesday Go over your MA 108 final exam and correct it.
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