(d^2)/(dx^2)(-(2x^2)/(5y^2))

Lösung

\frac{d ^{2}}{d x ^{2}} (- \frac{2 x ^{2}}{5 y ^{2}})

- \frac{4 ( y ^{2} - x ^{2} y \frac{d ^{2} y}{d x ^{2}} - 4 x \frac{d y}{d x} y + 3 x ^{2} \frac{d y}{d x} ^{2} )}{5 y ^{4}}

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} (- \frac{2 x ^{2}}{5 y ^{2}})

\frac{d}{d x} (- \frac{2 x ^{2}}{5 y ^{2}}) = - \frac{4 x ( - x \frac{d y}{d x} + y )}{5 y ^{3}}

= \frac{d}{d x} - \frac{4 x ( - x \frac{d y}{d x} + y )}{5 y ^{3}}

\frac{d}{d x} - \frac{4 x ( - x \frac{d y}{d x} + y )}{5 y ^{3}} = - \frac{4 ( y ^{2} - x ^{2} y \frac{d ^{2} y}{d x ^{2}} - 4 x \frac{d y}{d x} y + 3 x ^{2} \frac{d y}{d x} ^{2} )}{5 y ^{4}}

= - \frac{4 ( y ^{2} - x ^{2} y \frac{d ^{2} y}{d x ^{2}} - 4 x \frac{d y}{d x} y + 3 x ^{2} \frac{d y}{d x} ^{2} )}{5 y ^{4}}

\frac{d y}{d x} = e^{6 y + 10 x}

\frac{d}{d x} (2 x - \frac{16}{x ^{2}})

\int_{0}^{6} 2 x + 1 d x

\frac{d}{d t} (- t)

x^{2} - 2 x y + x \frac{d y}{d x} = 0