# calculus

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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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