d/(d{x)}({z}arctan(({y})/({x)}))

Solución

\frac{d}{d x} (z arctan (\frac{y}{x}))

- \frac{y z}{y ^{2} + x ^{2}}

Pasos de solución

\frac{d}{d x} (z arctan (\frac{y}{x}))

Sacar la constante:

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

= z \frac{d}{d x} (arctan (\frac{y}{x}))

Aplicar la regla de la cadena:

\frac{1}{( \frac{y}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{y}{x})

= \frac{1}{( \frac{y}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{y}{x})

\frac{d}{d x} (\frac{y}{x}) = - \frac{y}{x ^{2}}

= z \frac{1}{( \frac{y}{x} ) ^{2} + 1} (- \frac{y}{x ^{2}})

Simplificar

z \frac{1}{( \frac{y}{x} ) ^{2} + 1} (- \frac{y}{x ^{2}}) : - \frac{y z}{y ^{2} + x ^{2}}

= - \frac{y z}{y ^{2} + x ^{2}}

\frac{e ^{x}}{e ^{x} + 1}

y^{^{''}} + 5 y = - 180 x^{2} e^{5 x}

y^{^{'}} = \frac{( 4 t + y )}{( 4 y - t )}

x^{5} + 2, x + 2

\int sin (m x) d x