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Beliebt Rechnen >

(\partial)/(\partial y)(2xsin(x^2y))

Lösung

\frac{\partial}{\partial y} (2 x sin (x^{2} y))

Lösung

2 x^{3} cos (x^{2} y)

Schritte zur Lösung

\frac{\partial}{\partial y} (2 x sin (x^{2} y))

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= 2 x cos (x^{2} y) x^{2}

Vereinfache

2 x cos (x^{2} y) x^{2} : 2 x^{3} cos (x^{2} y)

= 2 x^{3} cos (x^{2} y)

Beliebte Beispiele

derivative of 5x^2+3x-2

steigung (-8,-14),(61,-32)

-(dy)/(dx)=4x^3y

limit as h approaches 0 of 1/(2^h)

d/(da)(a/(a^2+b^2))