Eli5: why are derivatives useful?

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I don’t mean in which cases I can use them, nor how they work. I know how they work (at least at a basic level, the derivative of ax\^b is abx\^(b-1), but I mean… why is a function that does those steps useful to solve any problem? It really seems like a random choice of operations.

In: Mathematics

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Anonymous 0 Comments

My mums house is 60 miles away and it takes me an hour, so on average I do 60mph on the journey there.

BUT if you have an equation that tells you where a car is along the road, you can get the derivative of that equation which will tell you it’s speed

So it’s slightly more detailed information than ’60mph’ which is what keeps my mum happy. She doesnt have the equation and doesnt know I did 80mph for some bits

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