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When a tractor-trailer turns a right-angle corner, the rear wheels follow a curve known as a tractrix, the equation for which is $y=\ln \left(\frac{1+\sqrt{1+x^{2}}}{x}\right)-\sqrt{1-x^{2}} \cdot$ Find $d y / d x$.

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 5

Derivative of the Logarithmic Function

Derivatives

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Okay, so we want to take her following Germany. But we first want to use log different stations. So let's take the natural log of oversights. So since we're taking the natural log, I'm gonna expand into what we have here on our right hand side by using our properties. Blawg, that is, we have the product X under square roots. So we can, you know, just as the natural log of X to the power of three. Bring down that three plus the natural log of one plus x two parts to this is the square root of that. That's too powerful in half. So I could bring down that one, huh? We now have the natural log. Why? And now let's take our full interpretive. So we're gonna have Why prime times One over why that's equal to derivative of the natural log. So that's one over X plus one half times 1/1 plus X squared times two acts. So what Kenyans office to So we get three over X thus X over one plus x squared. So now that's multiply both sides By why Now let's note that why was given to be X cubed times the square root of one plus X word, right? That is why is equal to the falling. So we got that wife time or d y over DX is equal to x cubed Time to square roots of one plus X squared all times three over x plus X over one plus X work.

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