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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2 x}{y}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (1) = 0

= \frac{1}{y} (2 x - 0)

Vereinfache

\frac{1}{y} (2 x - 0) : \frac{2 x}{y}

= \frac{2 x}{y}

Beliebte Beispiele

limit as x approaches 3 of 2x^{x^2}-3x+2

x \to 3 lim (2 x^{x^{2}} - 3 x + 2)

integral of-32x+12

\int - 32 x + 12 d x

y^{''}+y=2xcos(x)

y^{^{''}} + y = 2 x cos (x)

derivative of (sqrt(x)/(2-x))

\frac{d}{d x} (\frac{x}{2 - x})

derivative of [x+(x+sin^2(x)^3]^6)

\frac{d}{d x} ([x + (x + sin^{2} (x))^{3}]^{6})