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Beliebt Rechnen >

(\partial)/(\partial y)(xy(1/(y^3)+2))

Lösung

\frac{\partial}{\partial y} (x y (\frac{1}{y ^{3}} + 2))

Lösung

x (- \frac{2}{y ^{3}} + 2)

Schritte zur Lösung

\frac{\partial}{\partial y} (x y (\frac{1}{y ^{3}} + 2))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{\partial}{\partial y} (y (\frac{1}{y ^{3}} + 2))

Wende die Produktregel an:

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

f = y, g = \frac{1}{y ^{3}} + 2

= x (\frac{\partial}{\partial y} (y) (\frac{1}{y ^{3}} + 2) + \frac{\partial}{\partial y} (\frac{1}{y ^{3}} + 2) y)

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (\frac{1}{y ^{3}} + 2) = - \frac{3}{y ^{4}}

= x (1 \cdot (\frac{1}{y ^{3}} + 2) + (- \frac{3}{y ^{4}}) y)

Vereinfache

x (1 \cdot (\frac{1}{y ^{3}} + 2) + (- \frac{3}{y ^{4}}) y) : x (- \frac{2}{y ^{3}} + 2)

= x (- \frac{2}{y ^{3}} + 2)

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