derivative of axsin(2x+bxcos(2x))

Lösung

\frac{d}{d x} (a x sin (2 x) + b x cos (2 x))

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

Schritte zur Lösung

\frac{d}{d x} (a x sin (2 x) + b x cos (2 x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (a x sin (2 x)) + \frac{d}{d x} (b x cos (2 x))

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

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

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

\frac{d x}{d t} = - \frac{50}{π} x^{- \frac{3}{2}}

\int (sin (x) - 2 e^{x} + 3 x) d x

\int y^{2} (\frac{1}{y ^{5}} + \frac{y ^{4}}{2}) d y

d er i v a t i v e 6 x arcsin (x)

d er i v a t i v e (t + e^{t}) (9 - t)