derivative y=x^2sin^9(x)+xcos^{-4}(x)

Lösung

ableitung von

y = x^{2} sin^{9} (x) + x cos^{- 4} (x)

2 x sin^{9} (x) + 9 sin^{8} (x) cos (x) x^{2} + sec^{4} (x) + \frac{4 x sin ( x )}{cos ^{5} ( x )}

Schritte zur Lösung

\frac{d}{d x} (x^{2} sin^{9} (x) + x cos^{- 4} (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{2} sin^{9} (x)) + \frac{d}{d x} (x cos^{- 4} (x))

\frac{d}{d x} (x^{2} sin^{9} (x)) = 2 x sin^{9} (x) + 9 sin^{8} (x) cos (x) x^{2}

\frac{d}{d x} (x cos^{- 4} (x)) = sec^{4} (x) + \frac{4 x sin ( x )}{cos ^{5} ( x )}

= 2 x sin^{9} (x) + 9 sin^{8} (x) cos (x) x^{2} + sec^{4} (x) + \frac{4 x sin ( x )}{cos ^{5} ( x )}

\int \frac{1}{x ^{2} 4 x ^{2} + 9} d x

d er i v a t i v e f (x) = 6 x^{3} - \frac{27}{2} x^{2} + 3

d er i v a t i v e \frac{8}{7 x ^{2}}

d er i v a t i v e (5 x^{6} + 8 x^{3})^{4}

in v erse l a pl a ce \frac{2}{s ( 0.12 s + 1 )}