




A function f is differentiable at x_{0} if it looks like a straight line (called its tangent line sufficiently near x_{0}.Its derivative at x_{0 }is the slope of that line.It is denoted by f '(x_{0}) or and its formal definition is
Here is the slope of the secant line which approaches the slope of the tangent line as Dx approaches 0.
How small must Dx be so that is f '? Answer
The derivative is f 's "instantaneous" rate of change with respect to variable x.
If x is time and f represents position, then f ' is velocity.