derivative of e^x(acos(x+bsin(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

t an g e n t y = x^{2} - 4 x + 3, (1, 0)

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

\frac{d y}{d x} = 5 x e^{6 y}

a re a 3 x + 18, x^{2}

x \to 0 + lim (\frac{x ^{2} - 1}{x - 1})