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Beliebt Rechnen >

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

Lösung

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

Lösung

2 e^{y} x

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= e^{y} (2 x - 0)

Vereinfache

= 2 e^{y} x

Beliebte Beispiele

integral of-3sin(3x)

\int - 3 sin (3 x) d x

derivative (5x)^{9x}

d er i v a t i v e (5 x)^{9 x}

limit as t approaches 0 of tan(2t)

t \to 0 lim (tan (2 t))

limit as x approaches 2-of 2x^2+7

x \to 2 - lim (2 x^{2} + 7)

inverselaplace 2/(s^3+3s^2-4)

in v erse l a pl a ce \frac{2}{s ^{3} + 3 s ^{2} - 4}