derivative x^{-8cos(x)}

Lösung

ableitung von

x^{- 8 c o s (x)}

x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{- 8 c o s (x)})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{- 8 c o s (x)} = e^{(- 8 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 8 c o s (x)) l n (x)})

Wende die Kettenregel an:

e^{(- 8 c o s (x)) l n (x)} \frac{d}{d x} ((- 8 cos (x)) ln (x))

= e^{(- 8 c o s (x)) l n (x)} \frac{d}{d x} ((- 8 cos (x)) ln (x))

\frac{d}{d x} ((- 8 cos (x)) ln (x)) = 8 sin (x) ln (x) - \frac{8 cos ( x )}{x}

= e^{(- 8 c o s (x)) l n (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

Vereinfache

e^{(- 8 c o s (x)) l n (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x}) : x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

= x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

\frac{d}{d x} (4 x^{2} cos (2 x))

\frac{d y}{d x} = x + y - 1

in v erse l a pl a ce \frac{1}{s ^{3} ( s + 4 )}

\frac{d}{d x} (10 x^{10} e^{x})

\int \frac{1}{- t ^{2} + 8 t - 15} d t