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Question: Derivative with respect to a function

Question:Derivative with respect to a function

hendriksdf5 65 Maple 2024
differentiation diff
March 10 2025
1

I have calculated an expression which depends on functions. I would now like to calculate the derivative withe respect to a function  but when I try to do so I get the error “Deriving a functional ”Error, invalid input: diff received fA(r), which is not valid for its 2nd argument. There is no help page available for this error, so maybe someone knows what I am doing wrong .

I get this is because die diff function might not be able to handel a function as an argument, but how would I do it? 

> 

L := -r^2*((-fA(r)^4+(-2*fB(r)^2-2*fC(r)^2+2)*fA(r)^2+4*(D(fB))(r)*fA(r)*fC(r)*r-fB(r)^4+(-2*fC(r)^2+2)*fB(r)^2-4*fB(r)*fC(r)*(D(fA))(r)*r-2*r^2*(D(fA))(r)^2-1-2*r^2*(D(fB))(r)^2)/(2*g^2*r^4)+(r*(fB(r)^2+(1/2)*fC(r)^2+fA(r)^2-2*fA(r)+1)*H(r)^2+(-(D(K))(r)*r^2*fC(r)-2*K(r)*fB(r)*r)*H(r)+(1/2)*K(r)^2*fC(r)^2*r+(D(H))(r)*K(r)*r^2*fC(r)+r*((fB(r)^2+fA(r)^2)*K(r)^2+(1/2)*r^2*((D(H))(r)^2+(D(K))(r)^2)))*v^2/(r^2)^(3/2)-lambda((1/2)*(K(r)^2+H(r)^2-1)*v^2)^2)

-r^2*((1/2)*(-fA(r)^4+(-2*fB(r)^2-2*fC(r)^2+2)*fA(r)^2+4*(D(fB))(r)*fA(r)*fC(r)*r-fB(r)^4+(-2*fC(r)^2+2)*fB(r)^2-4*fB(r)*fC(r)*(D(fA))(r)*r-2*r^2*(D(fA))(r)^2-1-2*r^2*(D(fB))(r)^2)/(g^2*r^4)+(r*(fB(r)^2+(1/2)*fC(r)^2+fA(r)^2-2*fA(r)+1)*H(r)^2+(-(D(K))(r)*r^2*fC(r)-2*K(r)*fB(r)*r)*H(r)+(1/2)*K(r)^2*fC(r)^2*r+(D(H))(r)*K(r)*r^2*fC(r)+r*((fB(r)^2+fA(r)^2)*K(r)^2+(1/2)*r^2*((D(H))(r)^2+(D(K))(r)^2)))*v^2/(r^2)^(3/2)-lambda((1/2)*(K(r)^2+H(r)^2-1)*v^2)^2)

 (1)
> 

diff(L, fA(r))

Error, invalid input: diff received fA(r), which is not valid for its 2nd argument

  
 

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