Following functions: f(x_1, x_2)=[x_1x_2^2+x^3_1x_2 x^2_1x_2+x_1+x^3_2] g(u)=[e^u u^2+u] Is it possible to take a derivative of f(g) or g(f). If not - why?

Stacy Barr 2022-09-27 Answered
Following functions:
f ( x 1 , x 2 ) = [ x 1 x 2 2 + x 1 3 x 2 x 1 2 x 2 + x 1 + x 2 3 ]
g ( u ) = [ e u u 2 + u ]
Is it possible to take a derivative of f ( g ) or g ( f ). If not - why?
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Answers (1)

Zackary Galloway
Answered 2022-09-28 Author has 17 answers
f : R 2 R 2 and g : R R 2 .
Both functions are of class C on their domains, so we only need to know how composing the two functions makes sense. We can't compose g with f, but we can compose f with g and f g : R R 2 : it is a vector function, and ( f g ) ( u ) = J f ( g ( u ) ) g ( u ), where J f is the Jacobian matrix of f.
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