Alternate Definition of Derivative
limit (as x approaches a number c)=f(x)-f(c)/x-c x≠c
The alternate definition of derivative of a function is the rate of change of the function at a given point with respect to the change in its argument. In other words, it measures the instantaneous rate of change of the function at a particular point. This definition is usually represented as the limit of the difference quotient:
f'(a) = lim (f(x)-f(a))/(x-a), as x → a
where f(x) is the given function, a is the point at which we want to determine the derivative, and x is the argument that is approaching a. The derivative is calculated by taking the limit of the difference quotient as x approaches a. By doing this, we can find the slope of the tangent line at that point which represents the instantaneous rate of change of the function. This alternate definition of derivative is very useful in calculating the derivatives of functions that cannot be differentiated using the power rule or other basic techniques.
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