derivative of (x^2-2sin(x)+2xcos(x))

Lösung

\frac{d}{d x} ((x^{2} - 2) sin (x) + 2 x cos (x))

x^{2} cos (x)

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 2) sin (x) + 2 x cos (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} ((x^{2} - 2) sin (x)) + \frac{d}{d x} (2 x cos (x))

\frac{d}{d x} ((x^{2} - 2) sin (x)) = 2 x sin (x) + cos (x) (x^{2} - 2)

\frac{d}{d x} (2 x cos (x)) = 2 (cos (x) - x sin (x))

= 2 x sin (x) + cos (x) (x^{2} - 2) + 2 (cos (x) - x sin (x))

Vereinfache

2 x sin (x) + cos (x) (x^{2} - 2) + 2 (cos (x) - x sin (x)) : x^{2} cos (x)

= x^{2} cos (x)

x \to 2 lim (\frac{∣ x - 3 ∣}{x - 3})

\int tan^{3} (5 x) sec^{2} (5 x) d x

\frac{d}{d x} (\frac{1 + cos ( x )}{1 - cos ( x )})

\frac{d}{d x} (\frac{sin ( x )}{1 - cos ( x )})

\frac{d}{d θ} (sin (θ))