does finding a derivative mean that we are finding slope of a graph

Hello,

If you plot a curve on the co-ordinate plane (x-y axes), then the slope is given as the change in 'y' with respect to change in 'x'.

Mathematically, this is equal to (y2 - y1) / (x2 - x1).

This formula is only valid if the curve is a straight line, as the slope is same everywhere.

But for a curve, say graph of sin x, the slope is different at each point. In such cases, dy/dx (or the derivative) will give the slope of the curve "at that point". This is applicable to straight lines also.

For example, if I find derivative of sin x at 90 degrees, then it is the slope of the curve "at pi/2".

Hope this helps.
Thanks.