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Beliebt Rechnen >

(\partial)/(\partial y)(x^2e^{y^2})

Lösung

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

Lösung

x^{2} e^{y^{2}} \cdot 2 y

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= x^{2} e^{y^{2}} \cdot 2 y

Beliebte Beispiele

derivative of 5x^3sqrt(5x-2)

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

integral of 1-x^2+1/2 x^4

\int 1 - x^{2} + \frac{1}{2} x^{4} d x

taylor x^3-2x^2+3x-5,2

t a y l or x^{3} - 2 x^{2} + 3 x - 5, 2

limit as x approaches 4 of 2x^2-11x

x \to 4 lim (2 x^{2} - 11 x)

derivative of (42/(x^4))

\frac{d}{d x} (\frac{42}{x ^{4}})