WEBVTT
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in this problem, we have to find the equation
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for the tangent line to a curve and specifically were
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given a curve that is defined by a log rhythmic
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function. So we have the function. Why equals
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X square times the natural log of X and what
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we need to do before we confined the tangent line
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is find my prime. Well, how do we
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do that? We're going to have to apply the
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product rule. So why Prime would be equal to
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d X square dx times the national log of X
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plus x squared times d natural log of X over
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d x So when you do that, we simplify
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just a little bit. We get why prime equals
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two x times the natural log of X plus x
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So we have the derivative. But we want to
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know the equation for the tangent line. So what
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do we have to do now? We need the
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slope of our tangent line at the point that we're
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told in the problem 10 so we can plug in
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our X value into y prime. So why prime
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would be equal to two times one times the natural
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log of one plus one, so we would get
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zero plus one, which equals one. And now
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we confined the tangent line very easily. We have
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this form. Why? Minus why not equals M
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times X minus X not. And then we could
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just plug in the X and Y coordinates from our
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point, so we would have y minus zero equals
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one times X minus one, and then we can
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simplify to get the tangent line equals Why equal toe
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X negative one x minus one. Excuse me.
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So I hope that this problem helped you understand how
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we can find the tangent line to a curb using
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differentiation, specifically finding the derivative of a of a
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logarithmic function.