what is the 50th derivative of f(x) = cos x ?

Question

please show work if possible

Answer 1

f'(x)=-sin(x)
f''(x)=-cos(x)
f'''(x)=sin(x)
f''''(x)=cos(x)
and so on till you get to 50, think it's -cos(x) but you should double-check

Answer 2

ok so the 2nd derivative is -sin, the 3rd is derivative of -sin which is -cos. 4th would be sin. then the pattern repeats
So it goes 1. cos, 2. -sin, 3. -cos, 4 sin and so on 5th cos, 6th -sin, 7th -cos. 8th sin, etc...
50 divided by 4 would be 12 with a remainder of 2
The cycle has revolved 12 times then you're at the
49th derivative for the beginning of the 13 cycle of the 4 pattern.
49 i.e. 1 would be cos. 50 i.e. 2 would be -sin.

Answer 3

The derivative of sin x is cos x, and the derivative of cos x is -sin x.
Hence, the derivative of -sin x is -cos x, and the derivative of -cos x is sin x.

For every four derivatives you take, you end up back where you started. Hence, the 48th derivative of cos x is cos x. Take two more derivatives, and you end up at -cos x.

The 50th derivative of f(x) is -cos x.

Answer 4

because i'm bored and have been missing math classes since graduating high school...

following the basic rules of trig functions and their derivatives...
f1(cos x) = -sin x
f1(sin x) = cos x

so...

f1(x) = -sin x
f2(x) = -cos x
f3(x) = sin x
f4(x) = cos x

so, go by 4's in a cycle that brings us to...

f48(x) = cos x
f49(x) = -sin x
f50(x) = -cos x

there's your answer!

Answer 5

f(x)=cos x
f'=-sin x
f"=-cos
f'"=sin x
f""=cos x
so every 4 deriviatives, you are back where you started. 48=4*12 so the 48th dericative is cos x

the 2nd derivative of cos x is -cos x
the answer is -cos(x)

Answer 6

try to figure out the pattern.. the derivatives for this one are so easy, you should realize the pattern right off.. good luck

Answer 7

The answer's 3.

Answer 8

lol if you cant do your own homework you shouldn't be in calculus I or precalc