f(x)= e^(-1/(sin^2(x)) , -pi/2<x<pi/2 , x=/=0
f(x)= 0 , x=0

Can someone explain to me what these ranges mean? Do they have any effect on the derivitive? THANKS!

2. Originally Posted by shmayer
f(x)= e^(-1/(sin^2(x)) , -pi/2<x<pi/2 , x=/=0
f(x)= 0 , x=0

Can someone explain to me what these ranges mean? Do they have any effect on the derivitive? THANKS!

$f'(x)= e^{\frac{-1}{sin^2x}} (\frac{-1}{sin^2x})'$

Find this separately:
$(-sin^{-2}x)' = 2 sin^{-3}x cos x$

Then combine. Good luck!

3. THANKS!
....if you can answer this, how would i find the second derivative? It would be the same as the first derivative just multiplied by the derivative of 2sin^-3(x)cosx..but how would i derive this ?? Thanks again