derivative of x^2sin^7(x+xcos^{-2}(x))

Lösung

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

2 x sin^{7} (x) + 7 sin^{6} (x) cos (x) x^{2} + sec^{2} (x) (1 + 2 x tan (x))

Schritte zur Lösung

\frac{d}{d x} (x^{2} sin^{7} (x) + x cos^{- 2} (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^{- 2} (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^{- 2} (x)) = sec^{2} (x) (1 + 2 x tan (x))

= 2 x sin^{7} (x) + 7 sin^{6} (x) cos (x) x^{2} + sec^{2} (x) (1 + 2 x tan (x))

4 y^{^{''}} + 2 y^{^{'}} + 2 y = 0

\frac{d}{d x} (x + x x)

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

\int sin (x) 2 x d x

n = 0 \sum \infty \frac{1 ^{n}}{3 ^{n}}