The nation's unemployment rate edged down in November to 5.8 percent of the work force, indicating the economy may be somewhat stronger than expected despite widespread forecasts of a recession, the government reported yesterday.

Although the drop, from a 6 percent rate the previous month, came as a surprise to some analysts, it did not alter predicitions that the nation is heading into a slump. Other major statistics have shown the economy is slowing.

However, the failure of the jobless rate to rise was expected to stiffen the reluctance of the Carter administration to propose an anti-recession tax cut as part of the fiscal 1981 budget it will send Congress in January.

President Carter is scheduled to make a final decision on the tax-cut issue within another two or three weeks, before the budget goes to press. Yesterday's jobless figures were the last to be published before that date.

The statistics came as, separately, several major New York banks cut their prime lending rates again yesterday, reducing the prime to 15 1/4 percent from 15 1/2 percent previously, apparently in response to flagging loan demand. f

At the same time, the Federal Reserve Board reported that consumers took on less new installment credit in October than they did the previous month, reflecting a fallout in auto sales and possibily in purchases of other big-ticket items.

The reduction in the prime rate marked the second dip in two weeks following the sharp surge in interest rates in the wake of the Fed's Oct. 6 credit-tightening. The prime is the rate banks charge their most credit-worthy corporate customers.

The drop in the jobless rate last month was accompanied by moderate rise in the number of new jobs in the economy. Total employment, measured by a survey of households, jumped by 353,000. Industry payrolls swelled by 218,000 jobs.

However, the figures included only about 30,000 of the 140,000 layoffs in the auto industry and none of the 13,000 frings resulting from plant shutdowns in the steel industry, both of which came after the November survey was taken. i

Analysts said these layoffs, along with others that are expected to occur in industries that are dependent upon auto and steel production, would show up in next month's report. The jobless rate for December is expected to rise.

Yesterday's report raised some eyebrowns among economists, many of whom had predicted the unemployment rate would begin edging up with the November figures. George L. Perry, a Bookings Institution analyst, said the economy may be stronger than thought.

However, Perry and several other economists surveyed late yesterday insisted that the prediction of a coming recession is "still the right forecast" despite the November improvement.

Although the overall jobless rate declined two-tenths of a percentage-point, the length of the average work-week in the manufacturing sector continued to shrink, and factory overtime levels failed to increase any.

The major beneficiaries of last month's decline in unemployment were women and blacks, particularly black teenagers. The jobless rates for most other categories of workers remained essentially unchanged.

Yesterday's figures were to be closely watched by the White House for signs that the recession has arrived in earnest, policymakers are uncertain about the outlook and are reluctant to recommend a tax cut without more definite signs.

The November rate of 5.8 percent is close to the level of joblessness that most economists now regard as "full employment" -- the lowest the jobless rate can be pushed by broad economic measures without exacerbating inflation.

The jobless rate has been hovering in the 6 percent-or-under range for more than a year. Most economic forecasts now predict the unemployment rate will climb to between 7 and 8 percent by this time next year.

The figures on consumer credit showed outstanding installment debt rose by $2.19 billion in October, compared to a jump of $4.45 billion the previous month. The October increase was the smallest since January, 1977.

The amount of new credit extended actually declined 3.4 percent over the month to a seasonally adjusted $27.7 billion. Repayments and other liquidations rose 5.5 percent to $25.51 billion.

The reduction in the prime rate yesterday left that key interest rate a half percentage point below the alltime high of 15 3/4 percent to which it rose in October and early November after the Fed's credit-tightening action. r

The Fed pushed interest rates up in a dramatic effort to dampen loan demand and rein in the growth of the nation's money supply, which had been contributing to inflation. Many economists now say that move has been successful.