derivative of sin^2(e^{sin^2(x}))

Lösung

\frac{d}{d x} (sin^{2} (e^{s i n^{2} (x)}))

e^{s i n^{2} (x)} sin (2 e^{s i n^{2} (x)}) sin (2 x)

Schritte zur Lösung

\frac{d}{d x} (sin^{2} (e^{s i n^{2} (x)}))

Wende die Kettenregel an:

2 sin (e^{s i n^{2} (x)}) \frac{d}{d x} (sin (e^{s i n^{2} (x)}))

= 2 sin (e^{s i n^{2} (x)}) \frac{d}{d x} (sin (e^{s i n^{2} (x)}))

\frac{d}{d x} (sin (e^{s i n^{2} (x)})) = cos (e^{s i n^{2} (x)}) e^{s i n^{2} (x)} sin (2 x)

= 2 sin (e^{s i n^{2} (x)}) cos (e^{s i n^{2} (x)}) e^{s i n^{2} (x)} sin (2 x)

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= e^{s i n^{2} (x)} sin (2 e^{s i n^{2} (x)}) sin (2 x)

\int 3 x cos^{3} (x^{2} + 2) d x

t an g e n t f (x) = x^{2}, at m (x) = - \frac{1}{2}

\frac{d}{d x} (r^{2} - 8 x^{2})

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

n = 1 \sum \infty (- 1)^{n} n^{- 3}