WEBVTT
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Let's find the equation of the tangent line to this
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curve at the 0.0 The slope of the tangent line
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is going to be the derivative at the point.
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So let's find the derivative and our function is a
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product. So we need to use the product rule
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. So we have the first X times, the
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derivative of the second. And to find the derivative
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of the second, we have to use the chain
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rule. So we would get E to the negative
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X squared times, the derivative of negative X squared
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, which is negative two x So so far we
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have the first times, the derivative of the second
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, and we need plus the second times the derivative
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of the first and the derivative of X is just
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one. Okay, we could simplify this, but
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we could also just plug in r zero. Now
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we're evaluating this derivative at X equals zero. We
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could substitute the number in and then simplify later.
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So we have zero times e to the negative zero
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squared times negative to time zero. That's just all
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zero plus e to the negative zero squared times one
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Each of the zero is one So the derivative is
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one that's going to be the slope of the tangent
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line. So now, to find the equation of
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the line, we can use the point slope form
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. Why minus y one equals M times X minus
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X one, and we can substitute our 0.0 in
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for X one and why one? So we have
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y minus zero equals the slope one times X minus
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zero and that simplifies to B y equals X.