(\partial)/(\partial y)((2x^2y)/(4+x^2y^2))

Lösung

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

\frac{2 x ^{2} ( 4 - x ^{2} y ^{2} )}{( 4 + x ^{2} y ^{2} ) ^{2}}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int sec^{2} (2 θ) d θ

\frac{\partial}{\partial z} (9 x sin (y - z))

y^{^{''}} + y^{^{'}} - 3 y = 6 sin (2 x)

(sin^{2} (2 x))^{^{'}}

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