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

Lösung

ableitung von

f (t) = 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)

t an g e n t \frac{2}{x}, at x = \frac{1}{4}

t an g e n t y = \frac{- 2 x}{x ^{2} + 1}, (1, - 1)

x \to 5 lim (3 x^{2} - 2 x - 7)

t an g e n t f (x) = 2 x^{2} + 5 x - 3, (1, 4)

\frac{d}{d x} (A x e^{- x} cos (2 x) + B x e^{- x} sin (2 x))