What are some real life applications of calculus?

Answer 1

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.