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偏导数计算器
分步计算偏导数
这个在线计算器将计算函数的偏导数，并显示步骤。您可以指定任意积分顺序。
Solution
Your input: find $$$\frac{\partial}{\partial y}\left(x^{2} y^{2}\right)$$$
Apply the constant multiple rule $$$\frac{\partial}{\partial y} \left(c \cdot f \right)=c \cdot \frac{\partial}{\partial y} \left(f \right)$$$ with $$$c=x^{2}$$$ and $$$f=y^{2}$$$:
$${\color{red}{\frac{\partial}{\partial y}\left(x^{2} y^{2}\right)}}={\color{red}{x^{2} \frac{\partial}{\partial y}\left(y^{2}\right)}}$$Apply the power rule $$$\frac{\partial}{\partial y} \left(y^{n} \right)=n\cdot y^{-1+n}$$$ with $$$n=2$$$:
$$x^{2} {\color{red}{\frac{\partial}{\partial y}\left(y^{2}\right)}}=x^{2} {\color{red}{\left(2 y^{-1 + 2}\right)}}=2 x^{2} y$$Thus, $$$\frac{\partial}{\partial y}\left(x^{2} y^{2}\right)=2 x^{2} y$$$
Answer: $$$\frac{\partial}{\partial y}\left(x^{2} y^{2}\right)=2 x^{2} y$$$
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