微分　x^n

$3$\displaystyle{{ $ {x}^{{\alpha}} $ }^{\prime }={\alpha}{x}^{ {\alpha}- 1 }}$
　 $3$a$ は－1以外の定数

公式の導出はPCサイトを参照のこと。

■計算例

$3$\displaystyle{\begin{array}{lll} { $ {x}^{4} $ }^{\prime } & =4{x}^{ 3- 1 } & \vspace{6}\\ & =4{x}^{3} & \vspace{6}\\ \end{array}}$

$3$\displaystyle{\begin{array}{lll} { $ \sqrt[3]{ {x}^{2} } $ }^{\prime } & ={ $ {x}^{ \frac{\hspace{2}2\hspace{2}}{\hspace{2}3\hspace{2}} } $ }^{\prime } & \vspace{6}\\ & ={x}^{ \frac{\hspace{2}2\hspace{2}}{\hspace{2}3\hspace{2}}- 1 } & \vspace{6}\\ & ={x}^{ - \frac{\hspace{2}1\hspace{2}}{\hspace{2}3\hspace{2}} } & \vspace{6}\\ & =\frac{\hspace{2}1\hspace{2}}{\hspace{2} {x}^{ \frac{\hspace{2}1\hspace{2}}{\hspace{2}3\hspace{2}} } \hspace{2}} & \vspace{6}\\ & =\frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt[3]{x} \hspace{2}} & \vspace{6}\\ \end{array}}$

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