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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

x \to 8 + lim (\frac{3}{x - 8})

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

d er i v a t i v e 2 5 x^{3}

t an g e n t f (x) = \frac{- 8 x}{x ^{2} + 1}, at x = 0

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