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Beliebt Rechnen >

(\partial)/(\partial x)(y+(1/(1/x+1/z)))

Lösung

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

Lösung

\frac{z ^{2}}{( x + z ) ^{2}}

Schritte zur Lösung

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

Vereinfache

y + (\frac{1}{\frac{1}{x} + \frac{1}{z}}) : y + \frac{x z}{z + x}

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

= 0 + \frac{z ^{2}}{( z + x ) ^{2}}

Vereinfache

= \frac{z ^{2}}{( x + z ) ^{2}}

Beliebte Beispiele

integral of x/(sqrt(1+x^2)+x)

\int \frac{x}{1 + x ^{2} + x} d x

limit as n approaches infinity of |n|

n \to \infty lim (∣ n ∣)

integral of e^{4/x}

\int e^{\frac{4}{x}} d x

fläche y=x,y= 1/(x^2),x=2

a re a y = x, y = \frac{1}{x ^{2}}, x = 2

y^'+(2y)/x =-4/x ,y(1)=3

y^{^{'}} + \frac{2 y}{x} = - \frac{4}{x}, y (1) = 3