derivative f(x)=e^xsin(x)-3e^xcos(x)

Lösung

ableitung von

f (x) = e^{x} sin (x) - 3 e^{x} cos (x)

4 e^{x} sin (x) - 2 e^{x} cos (x)

Schritte zur Lösung

\frac{d}{d x} (e^{x} sin (x) - 3 e^{x} cos (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (e^{x} sin (x)) - \frac{d}{d x} (3 e^{x} cos (x))

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

\frac{d}{d x} (3 e^{x} cos (x)) = 3 (e^{x} cos (x) - e^{x} sin (x))

= e^{x} sin (x) + cos (x) e^{x} - 3 (e^{x} cos (x) - e^{x} sin (x))

Vereinfache

e^{x} sin (x) + cos (x) e^{x} - 3 (e^{x} cos (x) - e^{x} sin (x)) : 4 e^{x} sin (x) - 2 e^{x} cos (x)

= 4 e^{x} sin (x) - 2 e^{x} cos (x)

\frac{d}{d x} (\frac{x ^{3} - a x}{b x})

f (t) = sin^{3} (t)

y^{^{''}} - y^{^{'}} - 2 y = 0

l a pl a ce t r an s f or m f (t) = 7 sin (4 (t + 2)) + 3 cos (4 t - 2)

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