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Question: How to differentiate a vector-valued function with D?

Question:How to differentiate a vector-valued function with D?

Rouben Rostamian 8028 Maple 2022
vector differentiation
December 26 2022
1

Given a vector-valued function z(u,v), I want to calculate the derivative of z with respect to its first argument by applying the D operator to it. I don't see how.  Any suggestions?

> 

restart;
> 

z := (u,v) -> < a(u,v), b(u,v) >;

proc (u, v) options operator, arrow; `<,>`(a(u, v), b(u, v)) end proc

Calculate the derivative of z with respect to its first argument:

> 

P := diff(z(u,v), u);

Vector(2, {(1) = diff(a(u, v), u), (2) = diff(b(u, v), u)})

Express P through the D operator:

> 

Q := convert(P, D);

Vector(2, {(1) = (D[1](a))(u, v), (2) = (D[1](b))(u, v)})

Question:  How do we obtain Q directly by applying the D operator to z

without the help of diff?  This one doesn't work:

> 

D[1](z)(u,v);
type(%, Vector);

(D[1](`<,>`))(a(u, v), b(u, v))*(D[1](a))(u, v)+(D[2](`<,>`))(a(u, v), b(u, v))*(D[1](b))(u, v)

false

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