Question

If f(x) = sin(sin(sin(...(sin(sin x))...)))
then then value of f '(180°) = .....

Answer 1

is that the derivative?

Answer 2

f'(x) is the first derivative of f(x)

Answer 3

i believe answer is 1

Answer 4

how?

Answer 5

i think its -1
and chain rule

Answer 6

well after derivating all of ur outer functions are \(\cos\) lets try it with an example

\[f(x)=\sin(\sin(\sin x)))\]\[f'(x)=[(\sin(\sin x))]' \ \cos(\sin(\sin x)))\]\[ \ \ \ \ \ \ \ = \cos x \ \cos(\sin x) \ \cos(\sin(\sin x))) \]\[f'(\pi)=\cos \pi \cos 0 \cos 0=-1\]

so @completeidiot is right answer is -1............:)

Answer 7

thanks mukushla
what about with "chain rule", @completeidiot, i want study it...

Answer 8

what i did was chain rule...

Answer 9

hohoho... sorry, i just knowed

Answer 10

np man....:)

Answer 11

Haha this is confusing! You guys are smart! XD lol