$$$- \frac{\sqrt{2}}{4 t^{\frac{3}{2}}}$$$的导数
您的输入
求$$$\frac{d}{dt} \left(- \frac{\sqrt{2}}{4 t^{\frac{3}{2}}}\right)$$$。
解答
对 $$$c = - \frac{\sqrt{2}}{4}$$$ 和 $$$f{\left(t \right)} = \frac{1}{t^{\frac{3}{2}}}$$$ 应用常数倍法则 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dt} \left(- \frac{\sqrt{2}}{4 t^{\frac{3}{2}}}\right)\right)} = {\color{red}\left(- \frac{\sqrt{2}}{4} \frac{d}{dt} \left(\frac{1}{t^{\frac{3}{2}}}\right)\right)}$$应用幂次法则 $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$，其中 $$$n = - \frac{3}{2}$$$:
$$- \frac{\sqrt{2} {\color{red}\left(\frac{d}{dt} \left(\frac{1}{t^{\frac{3}{2}}}\right)\right)}}{4} = - \frac{\sqrt{2} {\color{red}\left(- \frac{3}{2 t^{\frac{5}{2}}}\right)}}{4}$$因此，$$$\frac{d}{dt} \left(- \frac{\sqrt{2}}{4 t^{\frac{3}{2}}}\right) = \frac{3 \sqrt{2}}{8 t^{\frac{5}{2}}}$$$。
答案
$$$\frac{d}{dt} \left(- \frac{\sqrt{2}}{4 t^{\frac{3}{2}}}\right) = \frac{3 \sqrt{2}}{8 t^{\frac{5}{2}}}$$$A
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