Quandaries
and Queries 

Name: mussawar Who is asking: Student Level of the question: Secondary Question: why we take derivative of dependent variable with respect to independent variable .can we take the derivative of independent with respect to dependent.if not why. 

Hi Mussawar, One way to see what to expect is to think of the graph, and the graphical meaning of the derivative. As a graphical process, the derivative is the tangent line. This tangent line does not change if you turn the graph, flip the graph (to switch which axis is thought of as 'independent' etc). It is, of course, a very local event, so this is moving into what is usually called implicit differentiation. We may not know the explicit form of the function, or the range over which it is a function, but we do know the tangent line, the slope (even after we turned around the graph of the curve) etc. The only time something 'strange' will happen here are the small numerical issues which come up when a horizontal tangent line becomes a vertical tangent line (and we tend to say 1/0 is not defined even when we 'see' the tangent line in front of us!) Walter
