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Tuesday, 14 January 2014

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    and   y   .   From given condition  a relation between    x    and    y    can be found and differentiating this expression we can find

                   dy/dx   ,

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      .