(\partial)/(\partial x)(arccot(x/y))

Lösung

\frac{\partial}{\partial x} (arccot (\frac{x}{y}))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (arccot (\frac{x}{y}))

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

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

Vereinfache

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

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

\frac{d}{d x} (7 + 9 x)

x \to - 1.9 lim (2 sin (x))

x \to 1 - lim (\frac{4}{x - 1})

(x - 6) y^{^{'}} + y = x^{2} + 18

t \to 0 lim (\frac{tan ( 3 t )}{t})