Using Maple to check partial derivatives \302\251 Mike May, S.J., 2006 - maymk@slu.edu Edited by Russell Blyth - blythrd@slu.edu We can use Maple to compute derivatives for us, thus letting us check our hand computations. To show how to do this we first define a function. f := (x,y) -> x^2+3*x*y+5*x^3+2*sin(exp((y+1)/y^2)); We can then find a partial derivative with the diff command. fx := diff(f(x,y),x); We can take second derivatives by either taking the partial of the partial, or by using diff with two x's. fxx := diff(f(x,y),x,x); fxxA := diff(fx,x); Third partials work much the same way fxxx := diff(f(x,y),x,x,x); fxxxA := diff(fxx,x); fxxAx := diff(fxxA,x); With our function we can also take the partial derivative with respect to y. fy := diff(f(x,y),y); This is messy enough that we would like to see a worked solution rather than just the answer. For that we load the Student[Calculus1] package and use the DiffTutor command. with(Student[Calculus1]): TutorAnswer := DiffTutor(f(x,y),y); TutorAnswer; To work with the right hand side of TutorAnswer we use the rhs command. Fy := rhs(TutorAnswer); This lets us find mixed partials. Fyx := diff(Fy,x); fyx := diff(f(x,y),y,x); LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn