|
|
|
|
|
|
|
|
|
|
|
|
$$$x^{3} + y^{5}$$$ 對 $$$y$$$ 的導數
您的輸入
求$$$\frac{d}{dy} \left(x^{3} + y^{5}\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dy} \left(x^{3} + y^{5}\right)\right)} = {\color{red}\left(\frac{d}{dy} \left(x^{3}\right) + \frac{d}{dy} \left(y^{5}\right)\right)}$$常數的導數為$$$0$$$：
$${\color{red}\left(\frac{d}{dy} \left(x^{3}\right)\right)} + \frac{d}{dy} \left(y^{5}\right) = {\color{red}\left(0\right)} + \frac{d}{dy} \left(y^{5}\right)$$套用冪次法則 $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$，取 $$$n = 5$$$：
$${\color{red}\left(\frac{d}{dy} \left(y^{5}\right)\right)} = {\color{red}\left(5 y^{4}\right)}$$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
Please try a new game Rotatly