In Exercises 59–86, find the derivative of y with respect to the given independent variable.
71. y = log₂(5θ)

Evaluate the integrals in Exercises 39–56.

55. ∫dx/(2√x + 2x)

Evaluate the integrals in Exercises 33–54.

∫(from ln4 to ln9)e^(x/2)dx

41. Cooling soup Suppose that a cup of soup cooled from 90°C to 60°C after 10 min in a room where the temperature was 20°C. Use Newton’s Law of Cooling to answer the following questions.

a. How much longer would it take the soup to cool to 35°C?

Theory and Applications

L’Hôpital’s Rule does not help with the limits in Exercises 69–76. 

Try it—you just keep on cycling. Find the limits some other way.

69. lim (x → ∞) (√(9x + 1)) / (√(x + 1))

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

73. y = log₄ x + log₄ x²

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.

126. eʸ = y^(ln x)