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Beliebt Rechnen >

(\partial)/(\partial x)(9xsin(5x^2y))

Lösung

\frac{\partial}{\partial x} (9 x sin (5 x^{2} y))

Lösung

9 (sin (5 x^{2} y) + 10 x^{2} y cos (5 x^{2} y))

Schritte zur Lösung

\frac{\partial}{\partial x} (9 x sin (5 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 9 \frac{\partial}{\partial x} (x sin (5 x^{2} y))

Wende die Produktregel an:

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

f = x, g = sin (5 x^{2} y)

= 9 (\frac{\partial}{\partial x} (x) sin (5 x^{2} y) + \frac{\partial}{\partial x} (sin (5 x^{2} y)) x)

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

\frac{\partial}{\partial x} (sin (5 x^{2} y)) = cos (5 x^{2} y) \cdot 10 y x

= 9 (1 \cdot sin (5 x^{2} y) + cos (5 x^{2} y) \cdot 10 y xx)

Vereinfache

9 (1 \cdot sin (5 x^{2} y) + cos (5 x^{2} y) \cdot 10 y xx) : 9 (sin (5 x^{2} y) + 10 x^{2} y cos (5 x^{2} y))

= 9 (sin (5 x^{2} y) + 10 x^{2} y cos (5 x^{2} y))

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