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1. Find the derivative of f(x) = (1 + 8x^2)(x – x^2) in two ways.
2. Differentiate. G(t) = t^4 cos t
3. Differentiate. F(x) = 9sqrt(x) sin x
4. Differentiate. F(x) = sin x + 3/4 cot x
5. Differentiate. Y = x^5/1-x^4
6. Differentiate. Y = 6x/9 – tan x
7. Differentiate. f(theta) = sec theta/4 + sec theta
8. Differentiate. F(y) = y/(y+(a/y))
9. Differentiate. Y = 5x^2 sin x tan x
10. Find an equation of the tangent line to the given curve at the specified point.
Y =( x^2 – 1)/(x^2 + x + 1), (1, 0)
11. If H(theta) = theta cos theta, find h’(theta) and H’’(theta).
12. Suppose f(pi/3) = 3 and f’(pi/3) = -5, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find the following.
13. Find the equations of the tangent lines to the curve.
Y = x-1/x+1 that are parallel to the line x -2y =3
14. A mass on a spring vibrates horizontally on a smooth level surface (see the figures). Its equation of motion is x(t) = 6 sin t, where t is in seconds and x is in centimeters.