derivative of (t(e^t(sin(t)+cos(t))))

Lösung

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

e^{x} (sin (x) + cos (x)) + 2 e^{x} x cos (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x} (sin (x) + cos (x)) + 2 e^{x} cos (x) x

Vereinfache

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

e x p an d \frac{1 + 10}{2}

e x p an d (x - \frac{1}{4}) (x - (-) \frac{2}{3})

e x p an d x + 3 2^{2}

s im pl i f y \frac{( x + 1 ) ^{2}}{x - 1}

s im pl i f y 2 (x - 3 y)