### 5.20 Der

• Der( <expression>, <variable>, <list> ).
• Description: this function calculate the derivative of the <expression> with respect to <variable> and evaluate it by giving to <variable> the values of the <list>. The function Der returns the list of results. But if we need the derivative’s expression, then we prefer the function Diff.
• Exemple(s)
• the command Der(1/x,x,[-1,0,2] ) returns [-1,-0.25].
• here is the text of a macro called tangente that takes an expression $f\left(x\right)$ as first parameter, a real value $x0$ as second parameter an that draw the tangent to the curve at the point x0 abscissa:
[Assign(%1,x,%2), \$A:=%2+i*%1, \$Df:=Der(%1,x,%2), Droite(A, A+1+i*Df)]

We assign the value $x0$ to the variable $x$ in the $f\left(x\right)$ expression, we store in the variable $A$ the point $\left(x0,f\left(x0\right)\right)$ (in affix format), we store in a variable $Df$ the derivative at $x0$ (${f}^{\prime }\left(x0\right)$), then we draw the straight line passing through $A$ with the direction of the vector whose affix is $1+i{f}^{\prime }\left(x0\right)$.