Nvidia (NVDA +1.91%) stock is posting big gains in Thursday's trading. The artificial intelligence (AI) hardware leader's share price was up 3.2% as of 2:25 p.m. ET and had been up as much as 3.6% earlier in the session.

Nvidia's valuation is on the rise today thanks to a major new business update from Taiwan Semiconductor Manufacturing (TSMC) and bullish momentum for the broader market. Because it manufactures Nvidia's semiconductor designs, TSMC's performance is often viewed as a bellwether for Nvidia -- and both companies' shareholders got some good news today.

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Is Nvidia stock a buy following TSMC's earnings beat?

Before the market opened this morning, TSMC published fourth-quarter earnings results that came in well ahead of Wall Street's expectations. The business posted non-GAAP (adjusted) earnings per share of $3.14 on sales of $33.7 billion, beating the average analyst estimate's call for a per-share profit of $2.98 on revenue of $32.73 billion.

TSMC's performance beats suggest that demand for the fabrication of AI chips remains very strong. In turn, this indicates that Nvidia is continuing to see very high demand for its processors and has continued to ramp up fabrication orders with the manufacturing leader.

With today's gains, Nvidia now has a market capitalization of approximately $4.59 trillion and is valued at roughly 21.5 times expected sales for the year and 40 times expected earnings. While the company's graphics processing units look poised to retain performance advantages over rival offerings, investors have been debating whether growth in AI infrastructure spending could begin to draw down this year. On the heels of TSMC's strong Q4 report, risk-tolerant investors have just gotten another buy signal on Nvidia stock.