# TI-Nspire CAS Calculus Submenu Commands

In the Calculus submenu of the TI-Nspire CAS, the CAS technology allows symbolic manipulation of algebraic expressions as well as numerical calculations just like in the Algebra submenu. The Derivative, Integral, and Limit commands form the cornerstone of the Calculus submenu. Here are some other items contained on the Calculus submenu that are worth mentioning, including a brief description of what they do:

**Tangent Line (& Normal Line):**The syntax for this command is tangentLine(*Expression*,*Variable*,*point*). This command returns the equation of the tangent line to the equation*y*=*expression*for an*x*-value equal to*point*. The Normal Line command works exactly the same way, except that it returns the equation of the line perpendicular to the tangent line at the same*point*on the curve*y*=*expression*.**Arc Length:**The syntax for this command is arclen(*Expression*,*Variable*,*Start*,*End*). This command gives the arc length of a function (given by*Expression*) from*x*=*Start*to*x*=*End*. Try evaluating arclen(*f*(*x*),*x*,*a*,*b*) to obtain the textbook formula for the arc length along a curve.**Differential Equation Solver:**The syntax for this command is deSolve(*1*^{st}*or 2*^{nd}*Degree Differential Equation*,*Independent Variable*,*Dependent Variable*). The commandreturns the general solution

*y*=*c*k*e*^{a}^{x}, where^{x}**k**is an integer suffix from 1 to 255. The first time you execute this command, TI-Nspire CAS returns the solution*y*=*c1**e*^{a}^{x}, where^{x}is an arbitrary constant.*c1*Subsequent occurrences of this arbitrary constant are denoted^{ },*c2*, and so on. To find a particular solution, include the initial condition(s) with the differential equation. For example, the command*c3*returns the solution

*y*=*e*^{a}^{x}.^{x}Press

and choose the apostrophe to denote a first derivative. Press

and choose the apostrophe again to denote a second derivative.

**Implicit Differentiation:**This command gives the implicitly defined derivative of an equation in which one variable is implicitly defined in terms of another variable. The syntax for this command is impDif(*Equation*,*Independent Variable*,*Dependent Variable*). For example, the commandreturns the result (2

*x**–**y)*/(x–2y).If a term such as

*xy*is in the equation, be sure to separate the variables by including multiplication (r) so that TI-Nspire CAS doesn’t think*xy*is its own variable.