No. The equation f(x)=x/6 is a stright line, with slope 1/6. Since the derivative of a function is its slope, this tells you that the derivative of f(x)=x/6 is f'(x) = 1/6.

You want to find the value for 'a' where the area between the curve y=x/6 and teh x-axis taken beween x=0 and x=a is equal to 1. If you've learned integrals (or "anti-derivatives") you can integrate y=x/6 and then solve for a point 'a' such that the definite integral between values of x=0 and x=a is equal to 1. But another way is to realize that the line y=x/6 forms a triangle with the x axis, and the area of that triangle it is one half base length tiomes height, or (1/2)xy. Sinc y = x/6, substitute this and solve for (1/2)x(x/6) = 1.