** The derivative of y = arctan(6x) is 6/(1 + 36 x^2).** To arrive at this answer, it is simply a matter of using the formula given for finding the derivative of the inverse tangent function. The formula is that for arctan (u) the derivative is du/(1 + u^2).

To find the derivative for arctan(6x), let u = 6x. Taking the derivative of "u" or du gives us that du = 6. By substituting back into the derivative formula du/(1+ u^2), the solution becomes 6/[1+ (6x)^2] or 6/(1 + 36 x^2).

Another way of expressing the formula for the derivative of the inverse tangent function is given as (d/dx)(arctanx) = 1/(1+x^2). Using tables of these inverse trigonometric functions and their derivatives makes solving these types of problems easier.