Find the derivative of the following function: y(x) = -3 sec 9 x.

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Presentation transcript:

Find the derivative of the following function: y(x) = -3 sec 9 x. -3 sec 9 x tan 9 x -27 sec 9 x tan 9 x -26 sec 9 x sin 9 x -27 sec 9 x cos 9 x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find an equation of the tangent line to the following curve at the given point: y = 3 sin (sin (x)), ( {image} , 0). 1. {image} y(x) = x + 3 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Suppose that F(x) = f(g(x)) and g(3) = 16, g'(3) = 5, f'(3) = 10, and f'(16) = 18. Find F'(3). 23 90 240 288 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

If g(x) = f(f(x)), use the table to estimate the value of g'(4). x 3 3 If g(x) = f(f(x)), use the table to estimate the value of g'(4). x 3 3.5 4 4.5 5 f(x) 6.5 2.1 4.5 5.1 2.2 -4.2 -6.9 8.8 3.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Suppose y = f ( x ) is a curve that always lies above the x-axis and never has a horizontal tangent, where f is differentiable everywhere. For what value of y is the rate of change of y 5 with respect to x eighty times the rate of change of y with respect to x? 1. 2. {image} 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50