Applications of partial derivatives

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Partial derivatives have significant real-life applications in various fields, including physics and engineering. They are essential in formulating the wave equation, which describes how waves propagate through different media. The heat equation, another critical application, models the distribution of heat in a given space over time. Additionally, partial derivatives are used in the potential equation, which is vital in electrostatics and fluid dynamics. Understanding these applications can enhance comprehension of complex systems in science and technology.
Palack
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Dear Everybody!

I'm searching for some real life applications of partial derivatives. I would be very thankful, if you sent me some example.

Thanks from Hungary.
 
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The wave equation, the heat equation and the potential equation.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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