There would be no modern technology without it.
There would be no physics beyond the basic "high school" level.
Physics leads to technology.
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Yes if it was not practical it was not there. You can see the real life use on this link http://www.intmath.com/Applications-differentiation/Applications-of-differentiation-intro.php
Pretty much any serious statistical model or experiment on anything will use basic calculus to interpret data. Anything that exponentially grows or decays (radioactive matter, bacteria, population growth, etc.) Anything that's built to be structurally sound. Anything that uses the EM spectra (radio, microwaves, visible light, etc.) All scientific industries use calculus practically constantly. And on and on and on... In reality, it's rarely pure theoretical calculus that's being done. Rather, another branch of math based on and built from the principles and results of calculus is primarily used called differential equations. Don't forget integration, the other "half" of calculus. That is as equally important in your listed applications. Also, both theoretical and applied calculus use both differentiation and integration. Differentiation isn't a separate branch of maths, but one of the two major branches of calculus as a whole.
Suppose a cubic crystal is growing so that the side changes at the rate of 10mm per second when the side length is 20 mm. If I want to know how fast the volume of the cube is growing at that time, I must use the equation V=x^3 and take the implicit derivative with respect to t and solve for dV/dt. or Suppose a plane is headed on a course of 050 at 300 mph and another is headed due north at 500 mph. If you want to know how fast the direct distance between them is changing, you must use implicit differentiation. In short, for everyday going to the grocery store type activities you won't need implicit differentiation. For complicated problems involving different rates of change you need to use implicit differentiation.
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