It is formally defined by taking the limit as the spacing between points approaches zero of the difference quotient.
In complex analysis, this operation is well-defined if and only if the Cauchy-Riemann equations are satisfied. The entries of the Jacobian are all examples of this operation applied to a function. This operation is applied n times on a given function and is multiplied by "x minus x sub 0" in the numerator for the nth minus one term of a function's Taylor series expansion. The inflection point of a function can be found by setting 0 equal to this operation applied twice to the function. It is formally defined by taking the limit as the spacing between points approaches zero of the difference quotient. For 10 points, name this basic operation from calculus whose value represents the slope of the line tangent to the graph, whose inverse is the integral.
In complex analysis, this operation is well-defined if and only if the Cauchy-Riemann equations are satisfied.
derivative [accept word forms like "differentiation," accept all more specific answers, such as first derivative, directional derivative, partial derivative, etc]