$$$5 - 6 x^{4}$$$的导数
您的输入
求$$$\frac{d}{dx} \left(5 - 6 x^{4}\right)$$$。
解答
和/差的导数等于导数的和/差：
$${\color{red}\left(\frac{d}{dx} \left(5 - 6 x^{4}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(5\right) - \frac{d}{dx} \left(6 x^{4}\right)\right)}$$常数的导数是$$$0$$$:
$${\color{red}\left(\frac{d}{dx} \left(5\right)\right)} - \frac{d}{dx} \left(6 x^{4}\right) = {\color{red}\left(0\right)} - \frac{d}{dx} \left(6 x^{4}\right)$$对 $$$c = 6$$$ 和 $$$f{\left(x \right)} = x^{4}$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$$- {\color{red}\left(\frac{d}{dx} \left(6 x^{4}\right)\right)} = - {\color{red}\left(6 \frac{d}{dx} \left(x^{4}\right)\right)}$$应用幂次法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，其中 $$$n = 4$$$:
$$- 6 {\color{red}\left(\frac{d}{dx} \left(x^{4}\right)\right)} = - 6 {\color{red}\left(4 x^{3}\right)}$$因此，$$$\frac{d}{dx} \left(5 - 6 x^{4}\right) = - 24 x^{3}$$$。
答案
$$$\frac{d}{dx} \left(5 - 6 x^{4}\right) = - 24 x^{3}$$$A