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Beliebt Rechnen >

(\partial)/(\partial w)((z+w)x^{1/2})

Lösung

\frac{\partial}{\partial w} ((z + w) x^{\frac{1}{2}})

Lösung

x^{\frac{1}{2}}

Schritte zur Lösung

\frac{\partial}{\partial w} ((z + w) x^{\frac{1}{2}})

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= x^{\frac{1}{2}} \frac{\partial}{\partial w} (z + w)

Wende die Summen-/Differenzregel an:

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

= x^{\frac{1}{2}} (\frac{\partial}{\partial w} (z) + \frac{\partial}{\partial w} (w))

\frac{\partial}{\partial w} (z) = 0

\frac{\partial}{\partial w} (w) = 1

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

Vereinfache

= x^{\frac{1}{2}}

Beliebte Beispiele

derivative f(x)=sin(1/x)

d er i v a t i v e f (x) = sin (\frac{1}{x})

f(x)=2x^3-3x^2-12x+6

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 6

(\partial)/(\partial x)(4xcos(x)cos(y))

\frac{\partial}{\partial x} (4 x cos (x) cos (y))

integral from sqrt(2) to 2 of x/(x^2-1)

\int_{2}^{2} \frac{x}{x ^{2} - 1} d x

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\int 3 x x^{2} - 1 d x