If L cm is the length of a pendulum and t s the time of one complete swing, it is known that L = kt^2. If the length of the pendulum is increased by x%, x being small, find the corresponding percentage increase in time of swing.

My workings:

L = kt^2

dL/dt = 2kt

delta t = dt/dL x delta L

delta t = 1/2kt x x% = x/2kt%

The answer given is x/2%.

Where where where have I gone wrong?!