derivative of x^{-6cos(x})

Lösung

\frac{d}{d x} (x^{- 6 c o s (x)})

x^{- 6 c o s (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{- 6 c o s (x)})

Wende Exponentenregel an:

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

x^{- 6 c o s (x)} = e^{(- 6 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 6 c o s (x)) l n (x)})

Wende die Kettenregel an:

e^{(- 6 c o s (x)) l n (x)} \frac{d}{d x} ((- 6 cos (x)) ln (x))

= e^{(- 6 c o s (x)) l n (x)} \frac{d}{d x} ((- 6 cos (x)) ln (x))

\frac{d}{d x} ((- 6 cos (x)) ln (x)) = 6 sin (x) ln (x) - \frac{6 cos ( x )}{x}

= e^{(- 6 c o s (x)) l n (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x})

Vereinfache

e^{(- 6 c o s (x)) l n (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x}) : x^{- 6 c o s (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x})

= x^{- 6 c o s (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x})

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