calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?

2. Find the derivative of f(x) = |x + 2| at the point (1, 3)

3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15.

4. Find all values of x on the graph of f(x) = -2x3 + 15x2 - 12 at which there is a horizontal tangent line.

5. Find the equation of the tangent line to the graph of f(a) = -sec(a) at the point (0, -1)

6. Differentiate y = sin(x)tan(x).

7. Find f '(x) for f(x) = sin(x)cot(x).

8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x)

9. Find f '(x) for f(x) = xln(x) - 5ex.

10. Find f '(x) for f (x) = e(^lnx) + e^(x)ln(x)

11. Find the x-coordinate where the graph of the function f(x) = e^(-cosx) has a slope of 0.

12. If the slope of a strictly increasing function at the point (a, b) is 3, what is the slope of the inverse of the function at the point (b, a)?

13. If e^xy = 2, then what is dy/dx at the point (1, ln2)?
14. At what point(s) on the curve x^2 + y^2 = 9 is the tangent line vertical?

15. f(x)=sqrtsin(4x)

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I did a couple of these above. Do you have any ideas of your own we can check?

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