U2S2V01 The Product Rule.txt

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You may have learned in classical mechanics
that f equals ma.
A more powerful version of this formula
is that force is the time derivative of momentum, p,
which is, d by dt of the quantity m times v.
If the mass is constant, this is the familiar law, f equals ma.
That's because if we write the equation f
is the derivative of m times v, we
can factor out the constant m, and get
m times the derivative of velocity,
which is m times acceleration.
But what if the mass is not constant?
Let's look at an example.
Consider the NASA mission to send the rover Curiosity
to Mars.
Most of the mass of the rocket is a huge supply of fuel.
But as the fuel burns, the mass decreases.
The mass is a function of time.
To understand the force, we need to know
how to take the derivative of the product, m
of t times v of t.
So let's learn how to take the derivative of products.