The phrase 'exceedingly difficult task' is correct and usable in written English.
You can use it when you want to emphasize how extremely difficult a task is. For example: "I was assigned an exceedingly difficult task - writing a book in only three months."
He knows this will be an exceedingly difficult task.
Measuring the greatest depths in the Mariana Trench is an exceedingly difficult task, given the technical challenges of delivering instrumentation to such a remote location and then obtaining accurate readings.
She worked closely with Joyce in the exceedingly difficult task of reading and correcting proofs and with the French typesetters, who were generally unfamiliar with standard English, much less Joyce's complex wordplay and portmanteau words.
Even with a leadership truly committed to an inclusive multiethnic state, this may have been an exceedingly difficult task.
And while federal regulators have been on a long and difficult quest for balance, managing the nation's historically over-harvested commercial fishing grounds remains an exceedingly difficult task, not least because determining just how many fish are out there at any given time still requires a bit of groping in the darkness.
Measuring the quality of a hospital is an important but exceedingly difficult task.
Once again, though, a patchwork of local concerns and inconsistent state regulation is already making the task exceedingly difficult.
But Trump, who won in a crowded primary by obliterating nearly every rhetorical boundary, seems to find the task exceedingly difficult.
However, the innate discrepancies between objects and tasks make this exceedingly difficult, and many developers are forced to find their task sets through trial and error.
More importantly, task-contingent conscientiousness exerted a direct effect on transfer, when task demands became exceedingly difficult and dynamic.
That task has become exceedingly difficult as consumer tastes have splintered and as products proliferate.
