What is the 4,782,084th derivative of cosx?

Answer 1

It's cos(x)
4,728,084 is divisible by four.
Let f(x)=cox(x)
f'=-sin(x)
f''=-cos(x)
f'''=sin(x)
f''''=cos(x)

So - the 4th, 8th, 12th, etc. derivatives are all cos(x).

Answer 2

That's easy,
cosx
Every 4th derivative of cosx is itself cosx. Since 4,782,084 is a multiple of 4...

Answer 3

1st derivative of cos x is -sen x,
2nd derivative of cos x is -cos x,
3rd derivative of cos x is sin x,
4th derivative of cos x is cos x, the original function
which means that 4th, 8th,12th, 16th, ..... etc.derivatives of cos x will be cos x. As 4,782084 is divisible by 4, so the desired derivative will be cos x.

Answer 4

As I recall, all even numbered derivatives of cosine are cosine also (odd ones are sine). Since that number is an even derivative the answer must be cos x.

Answer 5

f'(x)=cosx-sinx f''(x)= -sinx-cosx because the spinoff of sinx = cosx and the spinoff of cosx= -sinx by technique of definition. set the equations =0 to discover your serious factors, increasing/lowering, concave up/concave down.

Answer 6

i can't find my book on derivatives so im doing this from head.
when you derive cosine it becomes sine and changes sign (+/-)
but when you derive sine it becomes cosine with no sign change so off the top of my head.
since 4,782,084 evenly divides by 4 i guess the answer is cos(x)
as in no changes.

Answer 7

orig: cos
1st -sin
2 -cos
3 sin
4 cos
5 -sin
6 -cos
7 sin
8 cos


You return to cosx every fourth time you take a derivative.
4,782,084 divides evenly by four, so the 4,782,084th derivative is cos(x)

Answer 8

cosx.
every 4th derivative of cosx is cosx (every 2nd is -cosx)

Answer 9

It's cos x because every 4th derivative of cos x is cos x.

Answer 10

let pi represent the usual mathematical pie (know what i mean?)

then when you differentiate cosx n times you will get cos(x+n(pi)/2).
Therefore, in your case n=4,782,084. Pluck that number in and viola.