derivative of xcos(x+sin(x))

Lösung

\frac{d}{d x} (x cos (x) + sin (x))

- x sin (x) + 2 cos (x)

Schritte zur Lösung

\frac{d}{d x} (x cos (x) + sin (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x cos (x)) + \frac{d}{d x} (sin (x))

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

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

= cos (x) - x sin (x) + cos (x)

Vereinfache

= - x sin (x) + 2 cos (x)

x \to c lim (5 + 3 (- 2))

\int (2 x + 3) cos (x^{2} + 3 x) d x

\int \frac{( cos ( θ ) - sin ( θ ) )}{cos ^{2} ( θ )} d θ

\frac{\partial}{\partial x} (- 2 y e^{- x})

\int - sin (x) - cos (x) d x