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?!