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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.