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Beliebt Rechnen >

(\partial)/(\partial y)(3xy+e^{-x^2y})

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial y} (3 x y) = 3 x

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

= 3 x - x^{2} e^{- x^{2} y}

Beliebte Beispiele

derivative of \sqrt[3]{x}-2

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

derivative of x^2-2xy+y^2

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

derivative of (1+e^{-x}^{-1})

\frac{d}{d x} ((1 + e^{- x})^{- 1})

integral from 0 to 5 of e^{-x}

\int_{0}^{5} e^{- x} d x

(x^2+1)(dy)/(dx)+3x(y-1)=0,y(0)=3

(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0, y (0) = 3