Suppose that the differentiable function y = f(x) has an inverse and that the graph of f passes through the point (2, 4) and has a slope of 1/3 there. Find the value of df⁻¹/dx at x = 4.

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

19. y = (sech θ)(1-ln(sech θ))

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

14. lim (t → 0) sin 5t / 2t

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

19. lim (θ → π/6) (sin θ - 1/2) / (θ - π/6)

Evaluate the integrals in Exercises 97–110.

101. ∫ (log₁₀x / x) dx

11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f=O(g) and g=O(f).

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

21. y=arccos(x²)