derivative y=x^2sin^7(x)+xcos^{-6}(x)

Lösung

ableitung von

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\int \frac{1}{- 20 x - 20 x} d x

x y^{^{'}} + (1 + 2 x^{2}) y = x^{3} e^{- x^{2}}

\frac{d}{d x} (sec (7 x))

\frac{d}{d x} (2 x (x + 1)^{2})

x \to 3 + lim (\frac{x}{3 x - x ^{3}})