derivative x^{-7cos(x)}

Lösung

ableitung von

x^{- 7 c o s (x)}

x^{- 7 c o s (x)} (7 sin (x) ln (x) - \frac{7 cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{- 7 c o s (x)})

Wende Exponentenregel an:

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

x^{- 7 c o s (x)} = e^{(- 7 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 7 c o s (x)) l n (x)})

Wende die Kettenregel an:

e^{(- 7 c o s (x)) l n (x)} \frac{d}{d x} ((- 7 cos (x)) ln (x))

= e^{(- 7 c o s (x)) l n (x)} \frac{d}{d x} ((- 7 cos (x)) ln (x))

\frac{d}{d x} ((- 7 cos (x)) ln (x)) = 7 sin (x) ln (x) - \frac{7 cos ( x )}{x}

= e^{(- 7 c o s (x)) l n (x)} (7 sin (x) ln (x) - \frac{7 cos ( x )}{x})

Vereinfache

e^{(- 7 c o s (x)) l n (x)} (7 sin (x) ln (x) - \frac{7 cos ( x )}{x}) : x^{- 7 c o s (x)} (7 sin (x) ln (x) - \frac{7 cos ( x )}{x})

= x^{- 7 c o s (x)} (7 sin (x) ln (x) - \frac{7 cos ( x )}{x})

ma c l a u r in \frac{1}{2 + 3 x}

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\int \frac{( e ^{\frac{1}{x}} )}{x ^{3}} d x

\int - 2 x e^{- x^{2}} d x

\int_{1}^{4} \frac{x ^{2} + 7}{5 x - x ^{2}} d x