  Co-rotating spots at different latitudes on the stellar surface generate
periodic photometric variability and can be useful proxies to detect
Differential Rotation (DR). DR is a major ingredient of the solar dynamo but
observations of stellar DR are rather sparse. In view of the Kepler space
telescope we are interested in the detection of DR using photometric
information of the star, and to develop a fast method to determine stellar DR
from photometric data. We ran a large Monte-Carlo simulation of differentially
rotating spotted stars with very different properties to investigate the
detectability of DR. For different noise levels the resulting light curves are
prewhitened using Lomb-Scargle periodograms to derive parameters for a global
sine fit to detect periodicities. We show under what conditions DR can
successfully be detected from photometric data, and in which cases the light
curve provides insufficient or even misleading information on the stellar
rotation law. In our simulations, the most significant period P1_{out} could be
detected in 96.2% of all light curves. Detection of a second period close to
P1_{out} is the signature of DR in our model. For the noise-free case, in 64.2%
of all stars such a period was found. Calculating the measured latitudinal
shear of two distinct spots \alpha_{out}, and comparing it to the known
original spot rotation rates shows that the real value is on average 3.2%
lower. Comparing the total equator-to-pole shear $\alpha$ to $\alpha_{out}$ we
find that $\alpha$ is underestimated by 8.8%, esp. the detection of DR for
stars with $\alpha$ < 6% is challenging. Finally, we apply our method to four
differentially rotating Kepler stars and find close agreement with results from
detailed modeling. Our method is capable of measuring stellar rotation periods
and detecting DR with relatively high accuracy and is suitable for large data
sets.
