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

Lösung

ableitung von

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

2 x sin^{6} (x) + 6 sin^{5} (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^{6} (x) + x cos^{- 4} (x))

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (x^{2} sin^{6} (x)) = 2 x sin^{6} (x) + 6 sin^{5} (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^{6} (x) + 6 sin^{5} (x) cos (x) x^{2} + sec^{4} (x) + \frac{4 x sin ( x )}{cos ^{5} ( x )}

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

\frac{d}{d x} (\frac{3 x ^{4}}{4})

\int \frac{2 x - 1}{x ^{2} - x - 12} d x

y^{^{''}} + 9 y = 5 e^{x} - 162 x

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