r(t) = 2 sin(t)i + 3 cos(t)j

Plug pi/6 into the derivative or r(t)

2cos(pi/6); – 3sin(pi/6)

To find the magnitude, use the Pythagorean theorem with the results from plugging pi/6 into r'(t).

sqrt((sqrt(3))^2 + (3/2)^2) = sqrt(3+(9/4))

Find a common denominator (should be 4) and solve from there.

sqrt( 12/4 + 9/4) = sqrt(21)/2

Then, simply place the sqrt part of it in the denominator and multiply the constant in front of the derivative functions

2*sqrt(3)/sqrt(21)i -3/sqrt(21)j