Alternate Definition of Derivative
limit (as x approaches a number c)=f(x)-f(c)/x-c x≠c
The derivative of a function at a particular point can be defined as the rate at which the function is changing at that point. Alternatively, we can define the derivative as the slope of the tangent line to the graph of the function at that point. This implies that the derivative measures the sensitivity of the output of a function to small changes in its input, or in other words, how fast the output is changing with respect to the input. Symbolically, the derivative of a function f(x) at a point x=a can be represented as f'(a) or dy/dx∣x=a. The derivative has numerous applications in calculus, physics, economics, and engineering.
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