(\partial)/(\partial v)({u}(v)(v)^2e^v)

Lösung

\frac{\partial}{\partial v} (u (v) (v)^{2} e^{v})

\frac{\partial}{\partial v} (u (v)) v^{2} e^{v} + (2 v e^{v} + e^{v} v^{2}) u (v)

Schritte zur Lösung

\frac{\partial}{\partial v} (u (v) (v)^{2} e^{v})

Wende die Produktregel an:

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

f = u (v), g = v^{2} e^{v}

= \frac{\partial}{\partial v} (u (v)) v^{2} e^{v} + \frac{\partial}{\partial v} (v^{2} e^{v}) u (v)

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

= \frac{\partial}{\partial v} (u (v)) v^{2} e^{v} + (2 v e^{v} + e^{v} v^{2}) u (v)

\frac{d}{d x} (\frac{d y}{d x}) = 0

d er i v a t i v e \frac{6 x ^{2} + 8 x + 2}{x}

\frac{\partial}{\partial x} (ln (\frac{y ^{9}}{x ^{7}}))

x \to 0 lim (+ (\frac{ln ( x )}{x}))

\frac{\partial}{\partial x} (x e^{- x})