(\partial)/(\partial y)(3xz^3e^{y^2})

Lösung

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

6 e^{y^{2}} x z^{3} y

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

= 3 x z^{3} \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

= 3 x z^{3} e^{y^{2}} \cdot 2 y

Vereinfache

= 6 e^{y^{2}} x z^{3} y

x \to 2 lim (4 x^{2} + x + 4)

\int_{0}^{\frac{π}{6}} (6 sec^{2} (x)) d x

2 y^{^{''}} + 4 y^{^{'}} - 7 y = 7 cos (2 x)

\int 1 + x d x

t an g e n t f (x) = e^{3 x}, at x = \frac{1}{3} ln (5)