Evaluate the 100th derivate of the given function at x=0.

-8
-1
8
0

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

Let, $y = f(x) = 4x^{3} - 8\cos x$

Let $y_n$ be the $n_{th}$ derivative.

It is clear that. $100_{th}$ derivative of. $4x^{3}$ will be zero.

$-8\cos x$ follows a pattern in its derivatives. $8\sin x , 8\cos x , -8\sin x , -8\cos x , ........$ After every 4 derivatives it repaeats.

$\dfrac {100}{4} = 25$ .Hence, after 25 cycles its repeats to the same, i.e, $y_{100} = -8\cos x = -8$ .Since, $x = 0.$

$ANSWER :\boxed{-8}$