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Beliebt Rechnen >

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

Lösung

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

Lösung

y cos (y) + sin (y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x sin (x)) = 0

\frac{\partial}{\partial y} (y sin (y)) = sin (y) + y cos (y)

= 0 + sin (y) + y cos (y)

Vereinfache

= y cos (y) + sin (y)

Beliebte Beispiele

integral of (6sqrt(x)-\sqrt[6]{x})

\int (6 x - 6 x) d x

y^{^{''}} = k^{2} y

derivative of (1-x/(2+x))

\frac{d}{d x} (\frac{1 - x}{2 + x})

derivative of (x+e^{2x}^3)

\frac{d}{d x} ((x + e^{2 x})^{3})

integral of (sec(x))^3

\int (sec (x))^{3} d x