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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Produktregel an:

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

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

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

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

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

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

\frac{\partial}{\partial x} (y^{5} - 4 x y)

y^{^{'}} = \frac{6 y ^{3}}{( 3 - 2 x ) ^{2}}, y (0) = - 1

\int_{0}^{1} ln (2 x) d x

\int (\frac{2}{x ^{2}}) d x

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