We carry out spatially resolved spectral analysis with a physical scale of $sim$10 pc in X-ray for the superbubble 30 Dor C, which has the largest diameter of $sim$80 pc and the brightest non-thermal emission in superbubbles for the first time. We aim at investigating spatial variation of the physical properties of non-thermal emission as detected in some supernova remnants in order to study particle acceleration in a superbubble. We demonstrated that non-thermal components are detected in all the regions covering the entire field of 30 Dor C. The spectra in the west region of 30 Dor C can be described with a combination of the thermal and non-thermal components while the spectra in the east region can be fitted with the non-thermal component alone. The photon index and absorption corrected intensity in 2-10 keV of the non-thermal component show spatial variation from $sim$2.0 to $sim$3.7 and (4-130) $times$ 10$^{-8}$ erg~s$^{-1}$~cm$^{-2}$~str$^{-1}$, respectively, and the negative correlation between the non-thermal physical properties is observed. The temperature and normalization of the thermal component also vary within a range of $sim$0.2-0.3 keV and $sim$0.2-7 $times$ 10$^{17}$ cm$^{-5}$ str$^{-1}$, respectively, and the positive correlation between the photon index and the normalization is also detected. We revealed the correlations in a supperbubble for the first time as is the case in SNRs, which suggests the possibility that the same acceleration mechanism works also in the supperbubble.
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