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

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)

Evaluate the integrals in Exercises 33–54.

∫(from ln3 to ln2) (e^x) dx

Solve the initial value problems in Exercises 55–58.

55. dy/dt = e^t sin(e^t − 2),y(ln 2) = 0

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.

33. y = ln(sec(lnθ))