#### notes

The derivative `(ds)/(dt)`, we mean the rate of change of distance s with respect to the time t. In a similar fashion, whenever one quantity y varies with another quantity x, satisfying some rule y= f(x) , then `(dy)/(dx)` (or f' (x)) represents the rate of change of y with respect to x and `(dy)/(dx)]_(x=x_0)` (or f′ (x0)) represents the rate of change

of y with respect to x at x = x_0 .

Further, if two variables x and y are varying with respect to another variable t, i.e., if x = f( t ) and y= g( t) , then by Chain Rule `(dy)/(dx) = (dy)/(dt)/(dx)/(dt)` , if `(dx)/(dt)` ≠ 0

Thus, the rate of change of y with respect to x can be calculated using the rate of change of y and that of x both with respect to t.