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Beliebt Rechnen >

(\partial)/(\partial x)(-1/4 (y^2+x^2))

Lösung

\frac{\partial}{\partial x} (- \frac{1}{4} (y^{2} + x^{2}))

Lösung

- \frac{x}{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (- \frac{1}{4} (y^{2} + x^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= - \frac{1}{4} \frac{\partial}{\partial x} (y^{2} + x^{2})

Wende die Summen-/Differenzregel an:

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

= - \frac{1}{4} (\frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (x^{2}))

\frac{\partial}{\partial x} (y^{2}) = 0

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

= - \frac{1}{4} (0 + 2 x)

Vereinfache

- \frac{1}{4} (0 + 2 x) : - \frac{x}{2}

= - \frac{x}{2}

Beliebte Beispiele

(\partial)/(\partial x)(e^{-3t}sin(x+5t))

\frac{\partial}{\partial x} (e^{- 3 t} sin (x + 5 t))

integral of (x^2)/(x^2+7)

\int \frac{x ^{2}}{x ^{2} + 7} d x

limit as x approaches 2 of (x^3)/2

x \to 2 lim (\frac{x ^{3}}{2})

integral from 1 to 3 of 1

\int_{1}^{3} 1

y^{^{''}} - y = t^{2}