Alternative form of the definition of the derivative
lim x->c. f(x)-f(c) / x-c
The alternative form of the definition of the derivative is:
f'(x) = lim h->0 (f(x+h) – f(x-h)) / (2h)
This definition uses the concept of a symmetric difference quotient, where we take the difference between the function values at x+h and x-h, and divide by twice the distance between these points. This definition has the advantage of producing a more accurate estimate of the derivative, especially for functions with uneven slopes or non-smooth points. However, it can also be more complicated to calculate than the standard definition of the derivative.
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