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

Soluzione

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

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

Fasi della soluzione

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

Considera

k, t, r

come costanti

Elimina la costante:

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

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

Applica la regola degli esponenti:

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

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

Applica la regola della catena:

- \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}))

Semplificare

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} )}

\frac{d}{d t} (t \cdot sin (t))

x y^{2} y^{^{'}} = x + 4

\frac{d}{d x} (3 cot (\frac{x}{8}))

\int z e^{2 z} d z

\int_{0}^{6} x^{3} x^{2} + 36 d x