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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

16 y^{^{''}} + 8 y^{^{'}} + y = x + 6

y (x + 5) + y^{^{'}} = 0

n = 1 \sum \infty \frac{x ^{n}}{n ^{n}}

x \to 0 lim (- (\frac{1}{x}))

\frac{\partial}{\partial x} (\frac{0.09 ( 5 ^{x} )}{x ^{3}})