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Beliebt Rechnen >

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

Lösung

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

Lösung

e^{y - z^{2}} x

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (y - z^{2}) = 1

= x e^{y - z^{2}} \cdot 1

Vereinfache

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

Beliebte Beispiele

derivative of ln(2+e^x)

\frac{d}{d x} (ln (2 + e^{x}))

integral from-1 to 1 of (2x)/((x+7)^2)

\int_{- 1}^{1} \frac{2 x}{( x + 7 ) ^{2}} d x

(\partial)/(\partial z)(2xyz)

\frac{\partial}{\partial z} (2 x yz)

6x^2y^'=y^'+3xe^{-y}

6 x^{2} y^{^{'}} = y^{^{'}} + 3 x e^{- y}

derivative of-1/2+7/5 x^3

\frac{d}{d x} (- \frac{1}{2} + \frac{7}{5} x^{3})