3-2-19
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We're going to use the official definition for derivative.
So limit as H goes to 0 bracket 1 -, 6, the quantity X + H ^2
minus bracket 1 -, 6 X squared all over H 1 - 6.
If we foil out that X + H ^2, we get X ^2 + 2 XH plus H ^2.
We're going to distribute the six -6, so we're going to get
limit as H goes to 0 of 1 - 6 X squared -12 XH minus six H ^2 -,
1 + 6 X squared all over H.
If we've done this correctly, every single term that doesn't
have an H in it better be canceling in that numerator, and
it does.
So we see that we're going to then cancel an H out of every
term.
So we end up with -12 X -6 H If H goes to zero, we end up with
just -12 X.
And it's specifying that we want the derivative at X equal -4.
So we're going to stick in -4 when we have that -12 X.
So we're going to get a +48.