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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{y}{z ^{2}}

Schritte zur Lösung

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

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

= 0 - \frac{y}{z ^{2}}

Vereinfache

= - \frac{y}{z ^{2}}

Beliebte Beispiele

integral of 1/(kx-nx^2)

\int \frac{1}{k x - n x ^{2}} d x

steigung (1.4)(-5)

s l o p e (1.4) (- 5)

integral of 6(sin(2x))/(sin(x))

\int 6 \frac{sin ( 2 x )}{sin ( x )} d x

integral of 1+3x+18x^2

\int 1 + 3 x + 18 x^{2} d x

limit as x approaches 0+of (ln(x)+1)/x

x \to 0 + lim (\frac{ln ( x ) + 1}{x})