derivative y=x^2sin^4(x)+xcos^{-6}(x)

Lösung

ableitung von

y = x^{2} sin^{4} (x) + x cos^{- 6} (x)

2 x sin^{4} (x) + 4 sin^{3} (x) cos (x) x^{2} + sec^{6} (x) + \frac{6 x sin ( x )}{cos ^{7} ( x )}

Schritte zur Lösung

\frac{d}{d x} (x^{2} sin^{4} (x) + x cos^{- 6} (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{2} sin^{4} (x)) + \frac{d}{d x} (x cos^{- 6} (x))

\frac{d}{d x} (x^{2} sin^{4} (x)) = 2 x sin^{4} (x) + 4 sin^{3} (x) cos (x) x^{2}

\frac{d}{d x} (x cos^{- 6} (x)) = sec^{6} (x) + \frac{6 x sin ( x )}{cos ^{7} ( x )}

= 2 x sin^{4} (x) + 4 sin^{3} (x) cos (x) x^{2} + sec^{6} (x) + \frac{6 x sin ( x )}{cos ^{7} ( x )}

d er i v a t i v e y = \frac{9}{x + 8}

in v erse l a pl a ce \frac{s ^{2}}{s ^{4} + 2 s ^{2} + 1}

d er i v a t i v e 2 - 7 x

\int \frac{1}{x ^{2}} - \frac{3}{x ^{4}} d x

l a pl a ce t r an s f or m 2 t e^{3 t} + 4 t^{2} e^{- 5 t}