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

Lösung

ableitung von

f (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)

\frac{\partial}{\partial x} (3 y^{6} sin (3 x))

d er i v a t i v e 13 sin (x)

d er i v a t i v e f (x) = \frac{1}{x + 4}

x \to 0 lim (\frac{3}{x})

\frac{\partial}{\partial x} (\frac{61}{7 + x ^{2} + y ^{2}})