Provide an appropriate response.Explain the idea of a related rate.
A. A function y = f(x) is a function of x, but if x can be expressed as a function of some other variable, such as time, t, then y is also a function of t, and the dependence of y on t is related to the dependence of x on t, which means, in turn, that the rate of change of y, dy/dt, is related to the rate of change of x, dx/dt, by the relation =
?
.
B. A function y = f(t) is a function of t, but y can generally be related to x if x is also a function of t; that is, dy/dt ? dx/dt.
C. A function x = f(t) is a function of t, but x can generally be related to y if y is also a function of t; that is, dx/dt ? dx/dy.
D. A function y = f(x) is a function of x, but if x can be expressed as a function of some other variable, such as time, t, then y is also a function of t, and the dependence of y on t is related to the dependence of x on t, which means, in turn, that the rate of change of y, dy/dt, is related to the rate of change of x, dx/dt, by the relation =
?
.
Answer: D
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