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Beliebt Rechnen >

(\partial)/(\partial x)(21x^3cos(7x^2y))

Lösung

\frac{\partial}{\partial x} (21 x^{3} cos (7 x^{2} y))

Lösung

21 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))

Schritte zur Lösung

\frac{\partial}{\partial x} (21 x^{3} cos (7 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 21 \frac{\partial}{\partial x} (x^{3} cos (7 x^{2} y))

Wende die Produktregel an:

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

f = x^{3}, g = cos (7 x^{2} y)

= 21 (\frac{\partial}{\partial x} (x^{3}) cos (7 x^{2} y) + \frac{\partial}{\partial x} (cos (7 x^{2} y)) x^{3})

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

\frac{\partial}{\partial x} (cos (7 x^{2} y)) = - sin (7 x^{2} y) \cdot 14 y x

= 21 (3 x^{2} cos (7 x^{2} y) + (- sin (7 x^{2} y) \cdot 14 y x) x^{3})

Vereinfache

21 (3 x^{2} cos (7 x^{2} y) + (- sin (7 x^{2} y) \cdot 14 y x) x^{3}) : 21 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))

= 21 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))

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