derivative of x^2sin^8(x+xcos^{-6}(x))

Lösung

\frac{d}{d x} (x^{2} sin^{8} (x) + x cos^{- 6} (x))

2 x sin^{8} (x) + 8 sin^{7} (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^{8} (x) + x cos^{- 6} (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{2} sin^{8} (x)) + \frac{d}{d x} (x cos^{- 6} (x))

\frac{d}{d x} (x^{2} sin^{8} (x)) = 2 x sin^{8} (x) + 8 sin^{7} (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^{8} (x) + 8 sin^{7} (x) cos (x) x^{2} + sec^{6} (x) + \frac{6 x sin ( x )}{cos ^{7} ( x )}

\int_{0}^{2 π} 6 x^{2} sin (\frac{x}{4}) d x

d er i v a t i v e x sin (\frac{2}{x})

\int \frac{3 x}{4 - x} d x

\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 2 x} d x

t \to 0 lim (\frac{( 3 e ^{t} - 3 )}{t})