(\partial)/(\partial y)(2x^{4y})

Lösung

\frac{\partial}{\partial y} (2 x^{4 y})

8 x^{4 y} ln (x)

Schritte zur Lösung

\frac{\partial}{\partial y} (2 x^{4 y})

Behandle

x

als Konstante

Entferne die Konstante:

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

= 2 \frac{\partial}{\partial y} (x^{4 y})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{4 y} = e^{4 y l n (x)}

= 2 \frac{\partial}{\partial y} (e^{4 y l n (x)})

Wende die Kettenregel an:

e^{4 y l n (x)} \frac{\partial}{\partial y} (4 y ln (x))

= e^{4 y l n (x)} \frac{\partial}{\partial y} (4 y ln (x))

\frac{\partial}{\partial y} (4 y ln (x)) = 4 ln (x)

= 2 e^{4 y l n (x)} \cdot 4 ln (x)

Vereinfache

2 e^{4 y l n (x)} \cdot 4 ln (x) : 8 x^{4 y} ln (x)

= 8 x^{4 y} ln (x)