In Exercises 21–48, find the derivative of y with respect to the appropriate variable.
33. y=ln(arctan(x))

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

14. y = ln(2θ+2)

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

31. y=arccot(√t)

Let f(x) = x³ − 3x² − 1, x ≥ 2. Find the value of df⁻¹/dx at the point x = −1 = f(3).

Evaluate the integrals in Exercises 33–54.

53. ∫ (e^r / (1 + e^r)) dr

In Exercises 115–126, use logarithmic differentiation or the method in Example 6 to find the derivative of y with respect to the given independent variable.

124. x^(sin y) = ln y

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = e^(cost+lnt)