To find the derivative of the function y(x) = 5*arccot(2x), we can use the chain rule.

First, recall that the derivative of arccot(u) is -1/(1+u^2)*du.

Let u = 2x. So, arccot(2x) becomes arccot(u).

Now, the derivative of arccot(u) with respect to u is -1/(1+u^2).

Therefore, the derivative of y(x) = 5*arccot(2x) with respect to x is:

dy/dx = 5 (-1/(1 + (2x)^2)) 2
dy/dx = -10/(1 + 4x^2)

So, the derivative of the function y(x) = 5*arccot(2x) is:

y'(x) = -10/(1 + 4x^2)