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

Lösung

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

e^{y x} x y^{2} + 2 y e^{y x}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{y x}, g = y^{2}

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

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

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

= e^{y x} x y^{2} + 2 y e^{y x}

d er i v a t i v e f (x) = (x - 4) (x^{2} + 8)

y^{^{'}} = 4 y + y^{4}

\frac{d}{d x} (\frac{x ^{2} - 9 x + 14}{( x - 5 ) ( x - 10 )})

\frac{\partial}{\partial x} (y x^{- 1})

\frac{( x ^{2} + 1 ) d y}{d x} + 6 x (y - 1) = 0, y (0) = 6