Maharashtra State BoardHSC Arts 12th Board Exam
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Rate of Change of Bodies Or Quantities

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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. 

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Rate of Change Part 1 [00:21:05]
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