(\partial)/(\partial x)((-x^2)/(y^2))

Lösung

\frac{\partial}{\partial x} (\frac{- x ^{2}}{y ^{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{- x ^{2}}{y ^{2}})

Vereinfache

\frac{- x ^{2}}{y ^{2}} : - \frac{x ^{2}}{y ^{2}}

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{1}{y ^{2}} \cdot 2 x^{2 - 1}

Vereinfache

- \frac{1}{y ^{2}} \cdot 2 x^{2 - 1} : - \frac{2 x}{y ^{2}}

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

\frac{d ^{2}}{d x ^{2}} (6 sec (x))

\int \frac{x}{1 + x ^{2}} d x

f (x) = \frac{x ^{3}}{9}

\frac{d y}{d x} - 3 y = - 7 sin (x) - 7 cos (x)

x \to + 1 lim (e^{x - 1} - 1)