(\partial)/(\partial y)((x-y)/(x+z))

Lösung

\frac{\partial}{\partial y} (\frac{x - y}{x + z})

- \frac{1}{x + z}

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{x - y}{x + z})

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x) = 0

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

= \frac{1}{x + z} (0 - 1)

Vereinfache

= - \frac{1}{x + z}

\frac{d y}{d x} = 7 x y

x \to 0 lim (3 x + 4)

\int \frac{cos ^{3} ( x ) + 4}{cos ^{2} ( x )} d x

\int 3 sin^{2} (x) cos^{2} (x) d x

\frac{\partial}{\partial y} (\frac{- x - 7 y}{y ^{2} + 2 x ^{2}})