(\partial)/(\partial x)(1/(x^2-y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d y}{d x} = e^{5 x + 3 y}

y^{^{''}} + 4 y = 3 tan (2 x)

\int sin (2 x - 5) d x

\int_{0}^{2 π} 7 x^{2} sin (\frac{1}{4} x) d x

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