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I'm a student in chemical engineering and we use derivatives all the time. Basically we use them to measure how a system changes with time. Like in a chemical reaction of say, oxygen+hydrogen goes to water, we can use the derivative of the rate equation to measure how long it will take for a certain percentage of the reactants to be turned into products. This is vital for industrial processes.

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Q: What is the Real-life application of derivative?
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What is the Real life application of derivative?

As with any advanced math, whether you use it in your "real life" or not depends on whether you work in the engineering field or not. One very practical application of the derivative (for engineers) is to find the maximum (or minimum) of a function. Such maxima or minima can appear at points where the derivative is zero or undefined (also, at the endpoints of the range under consideration). Another application is to analyze the behavior of functions in general. This can assist you in graphing the functions.


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