(\partial)/(\partial x)((2pikt)/(ln(r/x)))

解

\frac{\partial}{\partial x} (\frac{2 πk t}{ln ( \frac{r}{x} )})

\frac{2 πk t}{x ln ^{2} ( \frac{r}{x} )}

解答ステップ

\frac{\partial}{\partial x} (\frac{2 πk t}{ln ( \frac{r}{x} )})

k, t, r

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 πk t \frac{\partial}{\partial x} (\frac{1}{ln ( \frac{r}{x} )})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= 2 πk t \frac{\partial}{\partial x} (ln^{- 1} (\frac{r}{x}))

連鎖法則を適用:

- \frac{1}{( ln ( \frac{r}{x} ) ) ^{2}} \frac{\partial}{\partial x} (ln (\frac{r}{x}))

= - \frac{1}{( ln ( \frac{r}{x} ) ) ^{2}} \frac{\partial}{\partial x} (ln (\frac{r}{x}))

\frac{\partial}{\partial x} (ln (\frac{r}{x})) = - \frac{1}{x}

= 2 πk t (- \frac{1}{( ln ( \frac{r}{x} ) ) ^{2}} (- \frac{1}{x}))

簡素化

2 πk t (- \frac{1}{ln ^{2} ( \frac{r}{x} )} (- \frac{1}{x})) : \frac{2 πk t}{x ln ^{2} ( \frac{r}{x} )}

= \frac{2 πk t}{x ln ^{2} ( \frac{r}{x} )}