y = cos(7x)
First derivative = -7sin(7x)
Second derivative = - (7^2)cos(7x)
3rd derivative = (7^3)sin(7x)
4th derivative = (7^4) cos(7x)
5th derivative = -(7^5) sin (7x)
6th derivative = -(7^6) cos(7x)
nth derivative ?
Analysis and conclusion
If n is multiple of 4 or a number before a multiple of 8 the sign is positive
If n is one or two numbers after a multiple of 4 the sign is negative.
7 is raised to exponent n
if n is odd the function is sin(7x), if n is even the function is cos(7x)
n = 57 => odd, and it is a number after 56 which is a multiple of 4 => negative sign
Therefore, the 57th derivative = - (7^57)sin(7x)
