Differentiation as rate measurer
dy/dx as rate measurer ;
dy/dx=(dy/dt)/(dx/dt) , if any two of
dy/dx , dy/dt and dx/dt are
given the value of the third can be determined
For working out problems there will be two variables x and y . From given condition a relation between x and y can be found and differentiating this expression we can find
Either dy/dt or dx/dt is given
Thus if dy/dt is given we can find dx/dt and vice versa .
If there is only one variable and its rate of change is given , then we can find the value of the variable in term of time t by integrating this expression .
We already know that ;
dy/dx=(dy/dt)/(dx/dt)=rate of change of (y)/rate of change of (x)
thus differential coefficient of y with respect to x is equal to the ratio of the rate of change of y and rate of change of x .