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

Solución

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

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

Pasos de solución

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

Tratar

k, t, r

como constantes

Sacar la constante:

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

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

Aplicar las leyes de los exponentes:

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

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

Aplicar la regla de la cadena:

- \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}))

Simplificar

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} )}