(\partial)/(\partial y)(x/(5+y))

Lösung

\frac{\partial}{\partial y} (\frac{x}{5 + y})

- \frac{x}{( 5 + y ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{x}{5 + y})

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{\partial}{\partial y} (\frac{1}{5 + y})

Wende Exponentenregel an:

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

= x \frac{\partial}{\partial y} ((5 + y)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 5 + y ) ^{2}} \frac{\partial}{\partial y} (5 + y)

= - \frac{1}{( 5 + y ) ^{2}} \frac{\partial}{\partial y} (5 + y)

\frac{\partial}{\partial y} (5 + y) = 1

= x (- \frac{1}{( 5 + y ) ^{2}} \cdot 1)

Vereinfache

x (- \frac{1}{( 5 + y ) ^{2}} \cdot 1) : - \frac{x}{( 5 + y ) ^{2}}

= - \frac{x}{( 5 + y ) ^{2}}

x \to - 1 lim (x - 1)

\frac{d ^{2}}{d t ^{2}} x + 5 \frac{d}{d t} x + 2 x = 0

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

x \to 0 lim (\frac{7 ^{x} - 2 ^{x}}{x})

y^{^{'}} + (6 x + \frac{1}{x}) y = 1