My personal favourite example is bond duration, which also gives insight into the meaning of a derivative.

The derivative of a function $f$ measures the sensitivity of $f(x)$ to a change in its input $x$. Functions whose derivatives are smaller are closer to being constant, so changing $x$ doesn't change $f(x)$ much, and vice versa.

The price of a bond is a function of its yield. The modified duration of a bond whose present value is $1$ is (minus) the first derivative of the bond price. It's one of the most important measures for bonds, because it tells you just what you would like to know when you buy a bond- namely how much interest rate risk you are taking on by buying it.