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A function f is differentiable at x0 if it looks like a straight
line (called its tangent line sufficiently near x0.Its derivative
at x0 is the slope of that line.It is denoted by f '(x0)
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.