Calculating the nth Derivative of Cos(X)

[trumpetplaya1687]

nth derivative!

I have a quick question...
what is the nth derivative of cos(X)?? I have written out the derivatives up to the 4th one...it being cos(X) as well, but i don't see the pattern for the nth because it continues to change between sin and cos. I'm doing this for Taylor Series. Thanks for any help.

 

[d_leet]

I have a quick question...
what is the nth derivative of cos(X)?? I have written out the derivatives up to the 4th one...it being cos(X) as well, but i don't see the pattern for the nth because it continues to change between sin and cos. I'm doing this for Taylor Series. Thanks for any help.

Well you have f(x) = cos(x) right

so

f'(x) = -sin(x) 1st derivative
f"(x) = -cos(x) 2nd derivative
f"'(x) = sin(x) 3rd derivative
f""(x) = cos(x) 4th derivative.
and it would repeat after this right...

see the pattern for a given n the nth derivative of cosine x can only be one of those 4 choices right.

so if n/4 has a remainder of 1 the nth derivative is -sin(x)
if n/4 has a remainder of 2 the nth derivative is -cos(x)
if n/4 has a remainder of 3 the nth derivative is sin(x)
if n/4 has a remainder of 0 ( n is divisible by 4) then the nth derivative is cos(x).

Does this help at all?