In Exercises 59–86, find the derivative of y with respect to the given independent variable.
73. y = log₄ x + log₄ x²

Airplane takeoff Suppose that the distance an aircraft travels along a runway before takeoff is given by D = (10/9)t², where D is measured in meters from the starting point and t is measured in seconds from the time the brakes are released. The aircraft will become airborne when its speed reaches 200 km/h. How long will it take to become airborne, and what distance will it travel in that time?

Which of the following statements about differentiation is true?

Given the initial-value problem: $\frac{d^{2}x}{d{t}^2}+c^{2}x=F_0\sin (ct)$, $x\left(0\right)=0$, $x^{\prime }\left(0\right)=0$, what is the general solution for $x\left(t\right)$?

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

11. y = 5x^(3.6)

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

77. y = log₃(((x + 1)/(x − 1))^(ln 3))

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

81. y = log₁₀(e^x)

Suppose that the function f and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.

Assuming the inverse function f^(-1) is differentiable, find the slope of f^(-1)(x) at

b. x=2

Suppose that the function f and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.

Assuming the inverse function f^(-1) is differentiable, find the slope of f^(-1)(x) at

c. x=3