Second Derivatives of Trigonometric Functions
This worksheet focuses on calculating second derivatives of trigonometric functions and their applications in calculus.
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Second Derivatives of Trigonometric Functions
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Read each question carefully and show all your work. Simplify your answers as much as possible.
1. Find the second derivative of the function f(x) = sin(2x).
2. Determine the second derivative of g(x) = cos(x^2).
3. If f(x) = tan(x), then f''(x) = .
4. The second derivative of y = csc(x) is .
5. Which of the following is the second derivative of f(x) = sec(x)?
sec(x)tan(x)
sec(x)tan^2(x) + sec^3(x)
sec^2(x)tan(x)
sec^2(x) + tan^2(x)
6. The second derivative of f(x) = sin(x) is -sin(x).
True
False
7. If y = cot(x), then y'' = 2cot(x)csc^2(x).
True
False
8. The position of a particle moving along the x-axis is given by s(t) = 3cos(t) - 2sin(t). Find the acceleration of the particle at t = π/2.