Inthepresentpaper,weobtainestimationsofconvergenceratederivativesoftheq-BernsteinpolynomialsBn(f,qn;x)approximatingtof′(x)asn→∞,whichisageneralizationofthatrelatingtheclassicalcaseqn=1.Ontheotherhand,westudytheconvergencepropertiesofderivativesofthelimitq-BernsteinoperatorsB∞(f,q;x)asq→1-.