University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 202: 68



Work Step by Step

$$5x^{4/5}+10y^{6/5}=15$$ $$x^{4/5}+2y^{6/5}=3$$ Using implicit differentiation, we differentiate both sides of the equation with respect to $x$: $$\frac{4}{5}x^{-1/5}+2\times\frac{6}{5}y^{1/5}\times y'=0$$ $$\frac{4}{5x^{1/5}}+\frac{12y^{1/5}}{5}\times y'=0$$ Now we set all elements with $y'$ to one side and the rest to the other side: $$\frac{12y^{1/5}}{5}\times y'=-\frac{4}{5x^{1/5}}$$ Finally, we calculate $y'$: $$y'=-\frac{\frac{4}{5x^{1/5}}}{\frac{12y^{1/5}}{5}}=-\frac{20}{60x^{1/5}y^{1/5}}$$ $$y'=-\frac{1}{3(xy)^{1/5}}$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.