The example of partial derivative that I chose is rocket acceleration with respect to fuel burn rate and exhaust velocity. It takes a lot of thrust to launch a rocket through the atmosphere and therefore it needs a lot of propellent/fuel.  The original mass of a rocket is about 90% fuel so over the force of the launch the mass is significantly decreasing while its acceleration is increasing. The rate which the fuel is burning is constant but since the mass of the rocket is changing the exhaust velocity is also changing, however not at a constant rate.  

References

OpenStax. (2016, August 3). 9.7 Rocket Propulsion. University  of Florida: General Physics Using Calculus I. Retrieved from  https://pressbooks.online.ucf.edu/phy2048tjb/chapter/9-7-rocket-propulsion/