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Beliebt Rechnen >

(\partial)/(\partial y)((x^2)/(y+2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

derivative of tan(2x^3)

\frac{d}{d x} (tan (2 x^{3}))

integral of x/(sqrt(x^4-16x^2+39))

\int \frac{x}{x ^{4} - 16 x ^{2} + 39} d x

fläche y=x+x^2+x^3,x=1

a re a y = x + x^{2} + x^{3}, x = 1

integral from 0 to e of a^x

\int_{0}^{e} a^{x} d x

(\partial)/(\partial v)(u^2-v^2)

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