Question

Find the 2021st derivative of f(x) = 2 cos(2x) a) 2 cos (2x) b) -2²⁰²¹ cos (2x) c) -2²⁰²¹ sin (2x) d) 2²⁰²¹ sin (2x)

Answer 1

To find the 2021st derivative of the function f(x) = 2cos(2x), differentiate it multiple times using the chain rule. The 2021st derivative is (-2)^2021cos(2x).

Step-by-step explanation:

To find the 2021st derivative of the function f(x) = 2cos(2x), we need to differentiate it multiple times. The derivative of cos(2x) with respect to x can be found using the chain rule, which states that the derivative of the composition of two functions is the derivative of the outer function multiplied by the derivative of the inner function.

So, the first derivative of f(x) = 2cos(2x) is f'(x) = -4sin(2x). Then, if we differentiate again, the second derivative is f''(x) = -8cos(2x).

By differentiating repeatedly, we can find that the 2021st derivative of f(x) = 2cos(2x) is (-2)^2021cos(2x). Therefore, the correct answer is option b) -2²⁰²¹cos(2x).