(\partial)/(\partial x)(2sqrt(x*y)-1/2 x^2)

Lösung

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

\frac{y}{x} - x

Schritte zur Lösung

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

Vereinfache

2 x y - \frac{1}{2} x^{2} : 2 x y - \frac{x ^{2}}{2}

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= \frac{y}{x} - x

f (t) = 6 sin (t)

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