(\partial)/(\partial y)(xsin(x/y))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int x sin (3 a x) d x

\frac{\partial}{\partial x} (x ln (z^{4} + x^{3}))

t an g e n t f (x) = (\frac{x + 3}{x - 3})^{2}, at x = 4

\frac{d}{d x} (ln (\frac{( 1 - x )}{1 + x}))

\int_{1}^{9} π (x - 1)^{2} d x