In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.
33. y = ln(sec(lnθ))

Show that the graph of the inverse of f(x)=mx+b, where m and b are constants and m≠0, is a line with slope 1/m and y-intercept -b/m.

Evaluate the integrals in Exercises 77–90.

81. ∫dy/(y²-2y+5)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

41. y= x arcsin(x) + √(1-x²)

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

18. y = t√(ln t)

Indeterminate Powers and Products

Find the limits in Exercises 53–68.

55. lim (x → ∞) (ln x)^(1/x)

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

27. lim (x → (π/2)^-) (x - π/2) sec x