The phrase 'develop a tendency' is correct and can be used in written English.
The phrase implies that something (typically a behavior or habit) is beginning to form or strengthen over time. For example, "After months of going to the gym, she had developed a tendency for healthy eating."
Rats trained under these conditions develop a tendency to emit extra lever presses during the time of heroin infusions (unreinforced responses).
The home fans began to voice their frustration as their side seemed to develop a tendency to play the ball backwards when an attack looked possible.
In the case of an environment characterised by the presence of strong wind, the tree will develop a tendency to produce reaction wood to change its centre of gravity so as to bring the stem to a vertical position (forming a curve).
"It is not hard to see how someone navigating that sort of neighborhood environment could develop a tendency to reflexively push back against being challenged," the paper continues.
The long-toothed matinee idol – that lesser-spotted showbusiness queen Keiran O'Nightley – has developed a tendency to shun the world.
Perhaps as a consequence, we've developed a tendency to downplay the importance of the human element in managing.
Under the new rule, it appears that chief executives of smaller companies developed a tendency to take option profits shortly before their stocks declined.
In some cases, original habitats were in present-day wintering areas, and animals developed a tendency to leave in spring in order to breed in other territories.
(Last year, Rove wrote a fan letter to a junior academic who had published a book pointing out that during the Civil War the Republican Party developed a "tendency to conflate Republicanism with loyalty and Democracy with treason").
Generally buoyant, Mr. McDermott has developed a tendency to note in rather mournful tones that Mr. Bradley is "a very serious guy who'd make a great president" and then begin reminiscing about Walter Mondale.
