You are here: TI-30X Pro MathPrint™ Scientific Calculator > Math Functions > Numerical Derivative

Numerical Derivative

The TI-30X Pro MathPrint™ calculates the (approximate) numerical derivative of an expression at a point given a tolerance for the numerical method. (See the About the Numerical Derivative at a Point section for more information.)

MathPrint™ Mode

% A pastes the numerical derivative template from the keypad to calculate the numerical derivative with the default tolerance H is 1EM5.

Example

% A

% A

z F T 5 z " "

M 1 <

To change the default tolerance, H, and observe how the tolerance plays a role in the numerical solution, paste the numerical derivative from the menu location, d MATH 7:nDeriv(, where the numerical derivative template will paste with the option to modify the tolerance as needed for an investigation of the numerical derivative result.

Example

d MATH 7:nDeriv(

with optional tolerance

d 7 z F T 5 z

" " M 1 " 1 E M 5

<

Classic Mode or Entry

In Classic mode or in classic edit lines, the nDeriv( command will paste from the keypad or MATH menu.

Syntax: nDeriv(expression,variable,point[,tolerance]) where tolerance is optional and the default H is 1EM5.

Example

% A

or

d MATH 7:nDeriv(

% A

z F T 5 z

% ` z

% ` M 1 )

<

About the Numerical Derivative at a Point

The numerical derivative at a point command, nDeriv( or d/dx, uses the symmetric difference quotient method. This method approximates the numerical derivative at a given point as the slope of the secant line about the point.

As H becomes smaller, the approximation usually becomes more accurate to approximate the slope of the tangent line at the given point x.

• Because of the method used to calculate the numerical derivative at a point, the calculator can return a false derivative value at a non-differentiable point.
• Always have some knowledge of the function behaviour near the point by using a table of values near the point (or a graph of the function).

³ Problem

Find the slope of the tangent line to the function f(x) = x2 - 4x at x = 2. What do you notice?

% A

z F U 4 z " "

2 <