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Beliebt Rechnen >

(\partial)/(\partial z)(xye^z+x-z^2-3)

Lösung

\frac{\partial}{\partial z} (x y e^{z} + x - z^{2} - 3)

Lösung

e^{z} x y - 2 z

Schritte zur Lösung

\frac{\partial}{\partial z} (x y e^{z} + x - z^{2} - 3)

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial z} (x y e^{z}) + \frac{\partial}{\partial z} (x) - \frac{\partial}{\partial z} (z^{2}) - \frac{\partial}{\partial z} (3)

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

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

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

\frac{\partial}{\partial z} (3) = 0

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

Vereinfache

= e^{z} x y - 2 z

Beliebte Beispiele

integral of 9/(x^2+4)

\int \frac{9}{x ^{2} + 4} d x

(\partial)/(\partial x)(6e^xln(y))

\frac{\partial}{\partial x} (6 e^{x} ln (y))

integral of xsin(x^2+1)

\int x sin (x^{2} + 1) d x

integral of (3n-4)/(n^2-2n)

\int \frac{3 n - 4}{n ^{2} - 2 n}

integral of ((1+xy)e^{xy})

\int ((1 + x y) e^{x y}) d x