SOLUTION: Choose a composite trigonometric function of the form h(x) = g(f(x)) where the function g is one of the trigonometric functions and f is any function more complicated than y = x.

Question 1093885: Choose a composite trigonometric function of the form h(x) = g(f(x)) where the function g is one of the trigonometric functions and f is any function more complicated than y = x.

Note: An example of an appropriate function h would be h(x) = sin(3x � 4). However, you must pick a function other than this example for this task.

1. Show the step-by-step computation of the correct derivative of h(x) using the chain rule.
2. Using the function h you constructed for part A, find the instantaneous rate of change at x = π/3.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Choose a composite trigonometric function of the form h(x) = g(f(x)) where the function g is one of the trigonometric functions and f is any function more complicated than y = x.
Note: An example of an appropriate function h would be h(x) = sin(3x � 4). However, you must pick a function other than this example for this task.
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Let g(x) = cos(x)
Let f(x) = 6x+20
Then h(x) = g(f(x)) = g(6x+20) = cos(6x+20)
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1. Show the step-by-step computation of the correct derivative of h(x) using the chain rule.
h'(x) = -sin(6x+20)*6 = -6sin(6x+20)
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2. Using the function h you constructed for part A, find the instantaneous rate of change at x = π/3.
h'(pi/3) = -6sin(6(pi/3)+20) = -6sin(20) = -6*0.9129 = -5.4777
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Cheers,
Stan H.
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