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Derivatives in Real Life
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You can use derivatives a lot in Newtonian motion where the velocity is defined as the derivative of the position over time and the acceleration, the derivative of the velocity over time.
What you can do with this?
You can use these properties to study the movement, for example, of your car if you know it's velocity at any instant, wihch is something doable. Another implementation of this kind of physics in daily life is the accelerometer built in your iPhone. This device can find how fast and to which direction you rotate your phone. That's how you can turn your phone to take a landscape oriented photo.
The most common use of the derivatives in math is for studying function. The most important theorem for studying functions is :
If f is a function defined on an interval I, and f′ it's derivative, then if f′>0 then f is increasing, if f′<0 then f is decreasing and if f′=0 then f has a minimum or maximum at that point.
This is a very important theorem let us study variations of functions. What about in everyday's life? Here is a situation :
One use of derivatives in chemistry is when you want to find the concentration of an element in a product. Here is the principle. For example: you have a solution S0 that you want to determinate it's concentration C0 in an element and you know that this solution gives an equivalence with the solution S1 with a concentration of C1.
When you plot the graph y=pH(V), you will notice a curve like the blue one. The red one is it's derivative.
Derivatives in Real Life
Derivatives are..
The derivative of a function of a real variable measures the sensitivity to change of a quantity which is a function and it's determined by another quantity.