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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

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

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

\int_{0}^{6} 36 - x^{2} d x

x \to 0 + lim (ln (ln (x)))

\frac{d y}{d x} = \frac{1}{sec ^{2} ( y )}

\frac{d}{d x} (\frac{x ^{4} + 2}{ln ( x )})

\int \frac{x}{e ^{4 x}} d x