Question

Find the 50th derivative of y=cos2x ?Find the 50th derivative of y=cos2x ?

Answer 1

To find the 50th derivative of y = cos(2x), use the chain rule and the fact that the derivative of cos(x) is -sin(x). The 50th derivative is sin(2x).

Step-by-step explanation:

To find the 50th derivative of y = cos(2x), we can use the chain rule and the fact that the derivative of cos(x) is -sin(x). The chain rule states that if y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).

In this case, let u = 2x. So, y = cos(u). Taking the derivative, we have dy/du = -sin(u). And since u = 2x, we can substitute back in to get dy/dx = -sin(2x).

Applying the chain rule 50 times, we get the 50th derivative: (-1)^25 * sin(2x) = sin(2x). So, the 50th derivative of y = cos(2x) is sin(2x).

Answer 2

The question is asking to find the 50th derivative of the equation y=cos2x, and in my further research and further calculation about the said equation, the 50th derivative of the equation is 2cos(2x), 2^50. I hope you are satisfied with my answer and feel free to ask for more if you have question