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Beliebt Rechnen >

(\partial)/(\partial x)(x^2+xe^{2y}-y)

Lösung

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

Lösung

2 x + e^{2 y}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 2 x + e^{2 y} - 0

Vereinfache

= 2 x + e^{2 y}

Beliebte Beispiele

(dx)/(dy)=4(x^2+1)

\frac{d x}{d y} = 4 (x^{2} + 1)

limit as x approaches infinity of (4x^3+8)/(4x^3+sqrt(64x^6+3))

x \to \infty lim (\frac{4 x ^{3} + 8}{4 x ^{3} + 64 x ^{6} + 3})

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

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

limit as x approaches 1 of 2x+2

x \to 1 lim (2 x + 2)

(d^2)/(dx^2)(x^{3/2})

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