I don't understand the algebra in this answer

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The forum discussion centers on the algebraic expression Δ(BA) = AΔ(B) when A is treated as a constant. The user seeks a proof for this relationship, which is derived from the expansion of Δ(AB) = (A+ΔA)(B+ΔB) - AB. By substituting ΔA = 0, the equation simplifies to AΔB, confirming the initial statement. The proof highlights the importance of understanding the behavior of constants in differential calculus.

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Homework Statement
At what average rate does the magnetic field need to change to induce emf of 1.0 V.
See attachment question 1.
Relevant Equations
See attachment solution.
Why does Δ(BA) = AΔ(B) when A is constant?
Is there a proof for this algebra?
Thanks
 

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Δ(AB) = (A+ΔA)(B+ΔB)-AB = AΔB+BΔA+ΔAΔB.
If A constant then ΔA=0, leaving only AΔB.
 
Thank you haruspex.
 

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