(\partial)/(\partial x)(-sin^2(x))

Lösung

\frac{\partial}{\partial x} (- sin^{2} (x))

- sin (2 x)

Schritte zur Lösung

\frac{\partial}{\partial x} (- sin^{2} (x))

Entferne die Konstante:

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

= - \frac{\partial}{\partial x} (sin^{2} (x))

Wende die Kettenregel an:

2 sin (x) \frac{\partial}{\partial x} (sin (x))

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

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

= - 2 sin (x) cos (x)

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= - sin (2 x)