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

Lösung

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

7 x^{6} y - 8 x^{3} y^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{6} y - 2 x^{3} y^{2}

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

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

\frac{\partial}{\partial x} (x^{6} y - 2 x^{3} y^{2}) = 6 y x^{5} - 6 y^{2} x^{2}

= 1 \cdot (x^{6} y - 2 x^{3} y^{2}) + (6 y x^{5} - 6 y^{2} x^{2}) x

Vereinfache

1 \cdot (x^{6} y - 2 x^{3} y^{2}) + (6 y x^{5} - 6 y^{2} x^{2}) x : 7 x^{6} y - 8 x^{3} y^{2}

= 7 x^{6} y - 8 x^{3} y^{2}

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e x p an d 2 sin (\frac{π}{4} (x - 5)) + 6

e x p an d (x^{2} + x + 1)^{5}

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