Question

How do you solve for higher order derivatives for example 90th derivative of cos(2x)

Answer 1

http://www.youtube.com/watch?v=wV1FrqwZyKw&feature=feedlik

Answer 2

Write out a couple of the first few derivatives:
f(x) = cos(2x)
f'(x) = -2sin(2x)
f''(x) = -4cos(2x)
f'''(x) = 8sin(2x)
f(4)(x) = 16cos(2x)
the key is to notice the pattern. Every 4 derivatives taken the expression reverts back to cosine. With every derivative the coefficient doubles. So the 88th derivative is a positive cosine, then the 90th must be a negative cosine, with the coefficient equal to 2^90
f(90)(x) = -(2^90)cos(2x)

Answer 3

thanks so much