In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.
70. y = ∛(x(x+1)(x-2)/(x²+1)(2x+3))

In Exercises 25–36, find the derivative of y with respect to the appropriate variable.

33. y = csch⁻¹(1/2)^θ

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

81. y = log₁₀(e^x)

In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then evaluate the limit using a method studied in Chapter 2.

3. lim (x → ∞) (5x² - 3x) / (7x² + 1)

Evaluate the integrals in Exercises 41–60.

43. ∫6cosh(x/2 - ln3)dx

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

19. lim(x→∞)arccsc(x)

Solve the initial value problems in Exercises 115–120.

115. dy/dx = 1/√(1 - x²), y(0) = 0