Question 2: Why does the implicit function derivative rule have continuous partial derivatives?
A:
The derivative is continuous to ensure the smoothness of the original function.
In this way, the derivative of the original function is always equal to the value of the derivative at this point.
Question 3: What is the derivative formula of mathematical implicit function? Derivation formula of implicit function:
FxFFdydyd2y
Implicit function F(x, y)? 02? (? x)+(？ x)？
dxFy？ xFy？ yFydxdxFyF？ z？ z
Implicit function F(x, y, z)? 0x
? xFz？ yFz
? f？ F(x，y，u，v)？ 0? (F，G)？ u
Implicit function equation: JG? (u，v)？ G(x，y，u，v)？ 0
? u
? u 1？ (F，G)？ v 1？ (F，G)？ xJ？ (x，v)？ xJ？ (u，x)？ u 1？ (F，G)？ v 1？ (F，G)？ yJ？ (y，v)？ yJ？ (u，y).