derivative sin^2(e^{sin^2(t)})

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Verwende die Doppelwinkelidentität:

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

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

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

\frac{d}{d x} ((6 x + 5)^{x})

n = 0 \sum \infty \frac{x ^{n}}{2 n !}

t a y l or e^{(- \frac{x}{2})}, 0

\frac{d}{d x} (e^{x} sin (5 x))