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Beliebt Rechnen >

(\partial)/(\partial y)(7x^{4y})

Lösung

\frac{\partial}{\partial y} (7 x^{4 y})

Lösung

28 x^{4 y} ln (x)

Schritte zur Lösung

\frac{\partial}{\partial y} (7 x^{4 y})

Behandle

x

als Konstante

Entferne die Konstante:

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

= 7 \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)}

= 7 \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)

= 7 e^{4 y l n (x)} \cdot 4 ln (x)

Vereinfache

7 e^{4 y l n (x)} \cdot 4 ln (x) : 28 x^{4 y} ln (x)

= 28 x^{4 y} ln (x)

Beliebte Beispiele

derivative of x^{-2}e^x

\frac{d}{d x} (x^{- 2} e^{x})

(dy)/(dx)=y^2*x^{-3}

\frac{d y}{d x} = y^{2} \cdot x^{- 3}

integral of 9xe^{-4x}

\int 9 x e^{- 4 x} d x

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\int (3 x z^{2} + 2) d z

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\frac{d}{d x} (lo g_{10} (\frac{x ^{2} - 1}{x}))