Function for approximation of the derivative based on the central difference method.
Natural Display input syntax is ^d_dx (f (x)) | x=a, while Linear Display input syntax is ^d_dx (f (x); a; tol).
tol specifies tolerance, which becomes 1 × 10-10 when nothing is input for tol.

Example 1: To obtain the derivative at point x = π/2 for the function y = sin(x)  (Angle unit: Rad)

(MthIO-MathO)

• ()(X)(π)2
• 0

(LineIO)

• ()(X)(;)(π)2
• 0

Example 2: ^d_dx (3x2 - 5x + 2; 2; 1 × 10-12) = 7  (LineIO)

• () 3(X)5(X)2(;)
  2(;) 112
• 7

Differential Calculation Precautions

Differential calculation can be performed in the COMP Mode only.

The following cannot be used in f(x): Pol, Rec, ÷R. The following cannot be used in f(x), a, b, or tol: ∫, d/dx, Σ.

When using a trigonometric function in f(x), specify Rad as the angle unit.

A smaller tol value increases precision, but it also increases calculation time. When specifying tol, use value that is 1 × 10-14 or greater.

If convergence to a solution cannot be found when tol input is omitted, the tol value will be adjusted automatically to determine the solution.

Non-consecutive points, abrupt fluctuation, extremely large or small points, inflection points, and the inclusion of points that cannot be differentiated, or a differential point or differential calculation result that approaches zero can cause poor precision or error.