derivative of x^5e^xcos(x)

Lösung

\frac{d}{d x} (x^{5} e^{x} cos (x))

5 x^{4} e^{x} cos (x) + (e^{x} cos (x) - e^{x} sin (x)) x^{5}

Schritte zur Lösung

\frac{d}{d x} (x^{5} e^{x} cos (x))

Wende die Produktregel an:

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

f = x^{5}, g = e^{x} cos (x)

= \frac{d}{d x} (x^{5}) e^{x} cos (x) + \frac{d}{d x} (e^{x} cos (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} e^{x} cos (x) + (e^{x} cos (x) - e^{x} sin (x)) x^{5}

in v erse l a pl a ce \frac{s - 3}{s ^{2} + 10 s + 9}

x \to 4 lim (2 x + 1)

d er i v a t i v e \frac{( x ^{8} )}{8 ( 1 - x ^{2} ) ^{4}}

\frac{d}{d x} (\frac{1}{( 9 + x ) ^{2}})

\frac{d}{d x} (ln (6 - 5 x))