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Beliebt Rechnen >

(\partial)/(\partial x)(2ysin(x)-x^3+ln(y))

Lösung

\frac{\partial}{\partial x} (2 y sin (x) - x^{3} + ln (y))

Lösung

- 3 x^{2} + 2 y cos (x)

Schritte zur Lösung

\frac{\partial}{\partial x} (2 y sin (x) - x^{3} + ln (y))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (2 y sin (x)) = 2 y cos (x)

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

\frac{\partial}{\partial x} (ln (y)) = 0

= 2 y cos (x) - 3 x^{2} + 0

Vereinfache

= - 3 x^{2} + 2 y cos (x)

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