derivative of 1/(x-y)

Lösung

\frac{d}{d x} (\frac{1}{x - y})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x - y})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x - y) = 1 - \frac{d y}{d x}

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

Vereinfache

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

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

\frac{d y}{d x} + \frac{1}{x} y = 0

\int 2 cos (\frac{x}{3}) d x

d er i v a t i v e f (x) = x^{2} - 6 x - 7

x y^{2} y^{^{'}} = y^{3} - 5 x^{3}

\frac{d}{d θ} (tan^{2} (θ))