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$$$x^{3} + y^{5}$$$ 关于 $$$y$$$ 的导数
您的输入
求$$$\frac{d}{dy} \left(x^{3} + y^{5}\right)$$$。
解答
和/差的导数等于导数的和/差：
$${\color{red}\left(\frac{d}{dy} \left(x^{3} + y^{5}\right)\right)} = {\color{red}\left(\frac{d}{dy} \left(x^{3}\right) + \frac{d}{dy} \left(y^{5}\right)\right)}$$常数的导数是$$$0$$$:
$${\color{red}\left(\frac{d}{dy} \left(x^{3}\right)\right)} + \frac{d}{dy} \left(y^{5}\right) = {\color{red}\left(0\right)} + \frac{d}{dy} \left(y^{5}\right)$$应用幂次法则 $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$，其中 $$$n = 5$$$:
$${\color{red}\left(\frac{d}{dy} \left(y^{5}\right)\right)} = {\color{red}\left(5 y^{4}\right)}$$因此，$$$\frac{d}{dy} \left(x^{3} + y^{5}\right) = 5 y^{4}$$$。
答案
$$$\frac{d}{dy} \left(x^{3} + y^{5}\right) = 5 y^{4}$$$A
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