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));

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We can then find a partial derivative with the diff command.

fx := diff(f(x,y),x);

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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);

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Third partials work much the same way

fxxx := diff(f(x,y),x,x,x); fxxxA := diff(fxx,x); fxxAx := diff(fxxA,x);

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With our function we can also take the partial derivative with respect to y.

fy := diff(f(x,y),y);

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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]);

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TutorAnswer := DiffTutor(f(x,y),y);

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TutorAnswer;

To work with the right hand side of TutorAnswer we use the rhs command.

Fy := rhs(TutorAnswer);

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This lets us find mixed partials.

Fyx := diff(Fy,x); fyx := diff(f(x,y),y,x);

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