(\partial)/(\partial x)(2cos^2(x))

Lösung

\frac{\partial}{\partial x} (2 cos^{2} (x))

- 2 sin (2 x)

Schritte zur Lösung

\frac{\partial}{\partial x} (2 cos^{2} (x))

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= 2 \cdot 2 cos (x) (- sin (x))

Vereinfache

2 \cdot 2 cos (x) (- sin (x)) : - 2 sin (2 x)

= - 2 sin (2 x)

\frac{\partial}{\partial y} (\frac{z}{x})

(x^{2} + 3) (\frac{d y}{d x}) = x y

\frac{d}{d x} (\frac{1}{( 5 x ^{6} + 4 x + 1 ) ^{\frac{9}{2}}})

\frac{d y}{d x} + \frac{6}{x} y = - 5 x + 9

(x + 1) \frac{d y}{d x} + (x + 2) y = 2 x e^{- x}