d/(dt)(acos(w(t)t)+bsin(w(t)t))

Lösung

\frac{d}{d t} (a cos (w (t) t) + b sin (w (t) t))

- 2 a wt sin (w t^{2}) + b cos (w t^{2}) \cdot 2 wt

Schritte zur Lösung

\frac{d}{d t} (a cos (w (t) t) + b sin (w (t) t))

Vereinfache

a cos (w (t) t) + b sin (w (t) t) : a cos (w t^{2}) + b sin (w t^{2})

= \frac{d}{d t} (a cos (w t^{2}) + b sin (w t^{2}))

Behandle

a, b, w

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (a cos (w t^{2})) + \frac{d}{d t} (b sin (w t^{2}))

\frac{d}{d t} (a cos (w t^{2})) = - 2 a wt sin (w t^{2})

\frac{d}{d t} (b sin (w t^{2})) = b cos (w t^{2}) \cdot 2 wt

= - 2 a wt sin (w t^{2}) + b cos (w t^{2}) \cdot 2 wt

\frac{d}{d x} (ln (\frac{x ^{3}}{x ^{5} + 1}))

d er i v a t i v e y = 10 + tan^{2} (x)

\int \frac{cot ( β )}{sin ^{6} ( β )} d β

\int \frac{1}{1 + \frac{1}{x}} d x

\frac{d}{d x} (4 x + 2)