One application of derivatives from first year calculus is something called differentials. The intent is to find the change of something based on the derivative of a function and some sort of varialbe like time or a distance or something.(adsbygoogle = window.adsbygoogle || []).push({});

Let's say you have this formula:

y = x^2

now here is the derivative:

dy/dx = 2x

now if you bring the dx over, it looks like this

dy = 2x dx

In math class, these are meant to find changes in things. Let's say you wanted to find the change in y when x changes from 5 to 10. you would just fill in the equation like this:

dy = 2(5)(5)

dy = 50

the dy is your change in y. the first 5 is your original x value. the second 5 is your change in x.

The differential said the change is 50. Now lets see what the original equation says the difference is:

final - original

= x^2 - x^2

= 10^2 - 5^2

= 100 - 25

= 75

The two different equations give VERY different answers. They're not even close. Knowing this, why do we still learn these?

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# Why do we learn differentials?

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