![image](https://www.icode9.com/i/l/?n=20&i=blog/2574235/202110/2574235-20211025172339644-232989152.png)
\[\frac{dx}{dy}=\frac{1}{f'(x)}
\]
\[\frac{d\frac{dx}{dy}}{dy}=\frac{d \frac{1}{f'(x)}}{dx} \cdot \frac{1}{\frac{dy}{dx}}=\frac{f''(x)\frac{-1}{[f'(x)]^2}}{f'(x)}=-\frac{f''(x)}{[f'(x)]^3}
\]
\[\frac{d \frac{dx^2}{d^2y}}{dy}=\frac{d \frac{dx^2}{d^2y}}{dx} \cdot \frac{1}{\frac{dy}{dx}}=\frac{-\frac{f'''(x)[f'(x)]^3-f''(x) \cdot f''(x) \cdot 3[f'(x)]^2}{[f'(x)]^6}}{f'(x)}=\frac{3[f'(x) \cdot f''(x)]^2-f'''(x)[f'(x)]^3}{[f'(x)]^7}
\]
标签:frac,cdot,微积分,随缘,2y,dx,dy
来源: https://www.cnblogs.com/nekko/p/15459580.html