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I've been working with differentiation for quite some time now, and I know how to use the product rule.

f(x) = u(x)*t(x)

f'(x) = u'(x)*t(x) + t'(x)u(x)

But what I don't understand is how one derives it...

Oh, and one more thing.

How do we know a number is irrational, likepiande?

Like, how do we know that it has an infinite number of decimals?

Is it because when you do the decimal operation you will eventually see that there's a sequence of decimals which repeats itself, or not? Something else perhaps?

Thanks in advance.

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# Proving the Product rule

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