“implicit differentiation”的概念、定义、翻译、参考文献-科学参考

implicit differentiation

Mathematics

单词	implicit differentiation
释义	implicit differentiation Mathematics When x and y satisfy a single equation, it may be possible to regard this as defining y as a function of x with a suitable domain (see implicit function theorem). Implicit differentiation involves applying the chain rule to obtain the derivative of y in such cases. For example, if xy² + x²y³−1=0, then $2 x y \frac{d y}{d x} + y^{2} + 3 x^{2} y^{2} \frac{d y}{d x} + 2 x y^{3} = 0$ and so, if 2xy + 3x² y² ≠ 0, $\frac{d y}{d x} = - \frac{y^{2} + 2 x y^{3}}{2 x y + 3 x^{2} y^{2}} .$
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