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.

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Presentation transcript:

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)) =

Derivative Rules Constant Multiplier Rule Sum and Difference Rule Product Rule Quotient Rule Chain Rule

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)

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)

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)

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 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.

Assignment for Wednesday Go over your MA 108 final exam and correct it.