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Beliebt Rechnen >

(\partial)/(\partial y)(xe^{9xy})

Lösung

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

Lösung

9 e^{9 x y} x^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (9 x y) = 9 x

= x e^{9 x y} \cdot 9 x

Vereinfache

x e^{9 x y} \cdot 9 x : 9 e^{9 x y} x^{2}

= 9 e^{9 x y} x^{2}

Beliebte Beispiele

fläche x+2,x^2-4

a re a x + 2, x^{2} - 4

(\partial)/(\partial x)(3y^2)

\frac{\partial}{\partial x} (3 y^{2})

integral of e^r(2+3e^r)^{3/2}

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

integral of cos(wnt)

\int cos (w n t) d t

derivative of y-5ln|y|+xy

\frac{d}{d x} (y - 5 ln ∣ y ∣ + x y)