By using linear response theory the low-temperature microwave response of a nonlocal and nonlinear d-wave superconductor with magnetic and nonmagnetic impurities is calculated. We will show that for the local, linear, and pure sample, penetration depth, <$E DELTA lambda (T)>, and conductivity, <$E DELTA sigma sub 1 (T)>, vary linearly with temperature, consequently the resistance, <$E DELTA R (T)>, would change linearly with temperature in agreement with experimental results and for the non-local, nonlinear sample the linear temperature dependences <$E DELTA R (T)> change to quadratic function. For impure samples the nonlocality and nonlinearity effects are completely hidden by impurities and the temperature dependences <$E DELTA lambda (T)> and <$E DELTA sigma sub 1 (T)> are determined by temperature interval namely the ranges of <$E T~<<~T sup *> and <$E T sup *~<<~T~<<~T sub c> which <$E T sup *> is determined by nonmagnetic impurity concentration and the strength of impurity scattering. For <$E T~<<~T sup *>, <$E DELTA R (T)> varies as <$E T sup 2>, on the other hand for, <$E T sup *~<< <<~T~<< <<~T sub c>, <$E DELTA R (T)> varies linearly with temperature. We will also show that the temperature dependence of surface resistance is unaffected by spin-orbit interaction and magnetic impurities.

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