Davis, 20, has made three Championship appearances this season, with his 7-146 against Glamorgan the best 2016 figures by a Derbyshire bowler.
Hemmings, also 20, made his first-class debut against Worcestershire in June.
"They will benefit greatly from another winter working with the first team," head coach John Sadler said.

The Commons Treasury Select Committee said the Financial Conduct Authority (FCA) made a serious error last year by mishandling a pre-briefing of its life insurance review.
Comments made by an FCA official in a newspaper interview sent insurers' share prices plunging.
Companies affected included Aviva, Legal & General and Prudential.
Clive Adamson, the head of supervision, said in the interview that the FCA would investigate whether people locked into pension plans were being treated unfairly.
That sparked fears about a possible effect on insurers' profits and prompted some investors to sell their stakes.
In a strongly worded 89-page report, the Treasury committee said the incident had been a "major self-inflicted distraction" from the FCA's core purpose of making markets function smoothly.
Andrew Tyrie, chairman of the committee, said: "By effectively breaching its own listing rules, the FCA itself created a false market in life insurance shares. Had a regulated firm behaved as the FCA did last March, the FCA is likely to have imposed a considerable fine."
However, the report stopped short of calling for resignations and instead set out several steps the watchdog should take over the next six months and report back.
The FCA said it was determined to learn the lessons and ensure this would never happen again, and would study the committee's recommendations.
The authority's executive committee, headed by chief executive Martin Wheatley, should examine communications methods and "poor working relationships" between divisions, the report said.
The board, headed by FCA chairman John Griffith-Jones, should commission an external review of its own effectiveness, according to the committee.
The FCA and the Bank of England's Prudential Regulation Authority should each produce a map setting out the responsibilities of senior officials in the same way the regulators are asking banks to, MPs said in the report.
They also called on the FCA to stop briefing certain journalists on forthcoming announcements unless it published the news at the same time any stories appeared in the media.
Further, the authority should train its staff on how to handle price-sensitive information.
"The evidence from this episode suggests that problems may still exist at the FCA. It is not yet clear to the committee that the FCA has fully grasped this," Mr Tyrie said.
The report echoes an independent inquiry by Simon Davis published in December that led to Mr Wheatley and other senior FCA officials losing their bonuses.
Mr Adamson left the FCA two days before the Davis report was published.

Mr Potts, who started his Tesco career at age 16 and rose to become retail director in the UK and chief executive of its Irish businesses, will take the helm on 16 March.
He takes over from Dalton Philips, who said in January he would leave the troubled supermarket after five years in charge.
The chain is battling falling sales.
It has been criticised for being slow in moving into the convenience store sector and setting up an online operation.
Current Morrisons chairman Andrew Higginson was previously the finance director at Tesco and worked with Mr Potts there for 15 years. He said was "delighted" by the appointment.
"David is the best retailer I have worked with in 25 years in the industry. Having worked alongside him for 15 years, I know he will bring to Morrisons a focus on the customer, a track record of delivery, flair, talent, and immense energy to his new role," he added.
Morrisons is being squeezed between the higher end of the market and the discount supermarkets chains.
The Bradford-based company reported a 3.1% drop in like-for-like sales in the six weeks to 4 January, and said it would close 10 loss-making stores this year.
Mr Potts will be tasked with returning the company to growth.
He said it "was an honour to have been selected".
Derbyshire pace bowler Will Davis and all-rounder Rob Hemmings have signed two-year contracts, keeping them with the county until 2018.
[NEXT_CONCEPT]
Britain's financial regulator created a false market in shares of life insurers last year, a group of MPs has said.
[NEXT_CONCEPT]
Morrisons has named former Tesco director David Potts as its new chief executive.