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Beliebt Rechnen >

(\partial)/(\partial y)(x^2-xy+9y^2)

Lösung

\frac{\partial}{\partial y} (x^{2} - x y + 9 y^{2})

Lösung

18 y - x

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2} - x y + 9 y^{2})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{2}) - \frac{\partial}{\partial y} (x y) + \frac{\partial}{\partial y} (9 y^{2})

\frac{\partial}{\partial y} (x^{2}) = 0

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

\frac{\partial}{\partial y} (9 y^{2}) = 18 y

= 0 - x + 18 y

Vereinfache

= 18 y - x

Beliebte Beispiele

(\partial)/(\partial x)(9e^{sqrt(xy)})

\frac{\partial}{\partial x} (9 e^{x y})

derivative of (e^{sqrt(ln(x)})^{2^{-x}})

\frac{d}{d x} ((e^{l n (x)})^{2^{- x}})

integral of (12)/(x^2-1)

\int \frac{12}{x ^{2} - 1} d x

derivative of (6x/(e^x))

\frac{d}{d x} (\frac{6 x}{e ^{x}})

integral of x^2cos(wx)

\int x^{2} cos (w x) d x