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Beliebt Rechnen >

(\partial)/(\partial y)(e^x+ye^{xy})

Lösung

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

Lösung

e^{x y} + e^{x y} x y

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= 0 + e^{x y} + x e^{x y} y

Vereinfache

= e^{x y} + e^{x y} x y

Beliebte Beispiele

(\partial)/(\partial x)(e^y+x+x^2+2)

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

(dy)/(-yln(y/k))=cdx

\frac{d y}{- y ln ( \frac{y}{k} )} = c d x

(dy)/(dx)+3y=30

\frac{d y}{d x} + 3 y = 30

y^{''}+9y=-6tan(3x)

y^{^{''}} + 9 y = - 6 tan (3 x)

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

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