derivative x^{-9cos(x)}

Lösung

ableitung von

x^{- 9 c o s (x)}

x^{- 9 c o s (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{- 9 c o s (x)})

Wende Exponentenregel an:

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

x^{- 9 c o s (x)} = e^{(- 9 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 9 c o s (x)) l n (x)})

Wende die Kettenregel an:

e^{(- 9 c o s (x)) l n (x)} \frac{d}{d x} ((- 9 cos (x)) ln (x))

= e^{(- 9 c o s (x)) l n (x)} \frac{d}{d x} ((- 9 cos (x)) ln (x))

\frac{d}{d x} ((- 9 cos (x)) ln (x)) = 9 sin (x) ln (x) - \frac{9 cos ( x )}{x}

= e^{(- 9 c o s (x)) l n (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x})

Vereinfache

e^{(- 9 c o s (x)) l n (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x}) : x^{- 9 c o s (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x})

= x^{- 9 c o s (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x})

\frac{d}{d x} (lo g_{e} (5 x))

\int \frac{1}{x ( 4 x )} d x

\int \frac{x ^{2}}{8 - x ^{3}} d x

\frac{d}{d t} (\frac{1}{2 + t})

y^{^{''}} + 2 y^{^{'}} = 8 x