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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

Beliebte Beispiele

sum from n=1 to infinity of 1/(2^{2n-1)}

n = 1 \sum \infty \frac{1}{2 ^{2 n - 1}}

integral of k/(x^6)

\int \frac{k}{x ^{6}} d x

derivative of 1/3 (x^2+2^{3/2})

\frac{d}{d x} (\frac{1}{3} (x^{2} + 2)^{\frac{3}{2}})

integral of-(4000x)/((1+x^2))

\int - \frac{4000 x}{( 1 + x ^{2} )} d x

integral of 3/(2+x)

\int \frac{3}{2 + x} d x