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Beliebt Rechnen >

(\partial)/(\partial x)(6y(3x^2-y^2))

Lösung

\frac{\partial}{\partial x} (6 y (3 x^{2} - y^{2}))

Lösung

36 y x

Schritte zur Lösung

\frac{\partial}{\partial x} (6 y (3 x^{2} - y^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 6 y \frac{\partial}{\partial x} (3 x^{2} - y^{2})

Wende die Summen-/Differenzregel an:

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

= 6 y (\frac{\partial}{\partial x} (3 x^{2}) - \frac{\partial}{\partial x} (y^{2}))

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

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

= 6 y (6 x - 0)

Vereinfache

= 36 y x

Beliebte Beispiele

derivative of (x^3-8/(x^2-4))

\frac{d}{d x} (\frac{x ^{3} - 8}{x ^{2} - 4})

(d^2)/(dx^2)((x^2+1)/(x-3))

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2} + 1}{x - 3})

derivative of (5+x^4^{12})

\frac{d}{d x} ((5 + x^{4})^{12})

integral of 1/(v^2+1)

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

inverselaplace (2s+1)/(3s^2+5s)

in v erse l a pl a ce \frac{2 s + 1}{3 s ^{2} + 5 s}