Final answer:
To find the 55th derivative of y = cos 2x, use the power rule for derivatives. The derivatives of cos 2x are -2sin 2x and -4cos 2x. Substitute these into the formula to find the 55th derivative.
Step-by-step explanation:
To find the 55th derivative of y = cos 2x, we can use the power rule for derivatives. The power rule states that if y = u^n, then the nth derivative of y with respect to x is given by the formula: y^(n) = n! * u^(n-1) * (du/dx)^n, where n! denotes the factorial of n.
In this case, u = cos 2x, so we need to find the first and second derivatives of cos 2x to use in the formula. The derivatives are: dy/dx = -2sin 2x and d^2y/dx^2 = -4cos 2x.
Now, we can substitute these derivatives into the formula to find the 55th derivative. Since n = 55, the 55th derivative of y = cos 2x is given by: y^(55) = 55! * (-4cos 2x)^(55-1) * (-2sin 2x)^55