derivative of e^{-2x}(acos(x+bsin(x)))

Lösung

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

- 2 e^{- 2 x} (a cos (x) + b sin (x)) + e^{- 2 x} (- a sin (x) + b cos (x))

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- 2 x}, g = a cos (x) + b sin (x)

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

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

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

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

Vereinfache

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

x \to 0 + lim (\frac{6}{sin ( x )})

\frac{d y}{d x} + x y = y

\frac{d}{d x} (cot (7 x))

\int \frac{1}{x ^{2}} - \frac{1}{x ^{3}} d x

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