Answered: Find dy if y = In* +1 7 -t dy dt

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.3: Quadratic Equations

Problem 51E

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$w e h a v e y = \ln (\frac{t^{2} + 1}{\sqrt{7 - t}}) H e n c e \frac{d y}{d t} = \frac{1}{(\frac{t^{2} + 1}{\sqrt{7 - t}})} \frac{d}{d t} (\frac{t^{2} + 1}{\sqrt{7 - t}}) = \frac{\sqrt{7 - t}}{(t^{2} + 1)} \frac{d}{d t} (\frac{t^{2} + 1}{\sqrt{7 - t}}) \frac{d y}{d t} = \frac{\sqrt{7 - t}}{(t^{2} + 1)} (\frac{2 t (\sqrt{7 - t}) - (t^{2} + 1) \times \frac{(- 1)}{2 \sqrt{7 - t}}}{{(\sqrt{7 - t})}^{2}}) = \frac{2 t (7 - t) + (t^{2} + 1) \times \frac{1}{2}}{(7 - t) (t^{2} + 1)} (F o r m u l a u s e d \frac{d}{d t} (\frac{u}{v}) = \frac{(\frac{d u}{d t} . v - u . \frac{d v}{d t})}{v^{2}})$

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