Problem

If $ x^2 + xy + y^3 = 1, $ find the value of $ y"…

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Problem 39 Hard Difficulty

If $ xy + e^y = e, $ find the value of $ y" $ at the point where $ x = 0. $

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Video Transcript

In this problem were given an equation and we're justified secondary to apply with respect to x and x is 0 point. So, let's first plug x, 0 in and let's see the value of the function y when x is 0. So we have 0 times y plus e to the y is equal to e. This term is 0. So from this we see that when x is 0 y is equal to 1. All right now to find the first zertho have less differentiate. Both sides of disrectxwe have y plus x times y prime plus e to the y times y prime is equal to 0 point from this. We see that then y prime is equal to negative y divided by x, plus e to y. When x is 0, we found that y is equal to 1 plus evoid derivative. At that point, so y prime would then be equal to negative 1 over 0 plus e to the 1, and that will be negative 1 over e all right now, using this y prime equation, we're going to differentiate the 1 more time to find second dative. We only use question rule o y double prime would then be equal to the negative of y prime times x, plus e to the y plus y times 1 plus e to the y times y prime divided by x, plus e to the y square. All right now, let's simulate y double prime secondary to y 1 x 0, that is negative, vita y prime, is equal to negative 1, or so we have negative 1 over e times 0 plus e plus 1 times 1 plus e times negative 1 over e divided By 0 plus e square now these will cancel out. This will cancel out and we don't find y double prime to be negative of negative 1 over square. So the answer is 1 over b square.

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Problem

If $ x^2 + xy + y^3 = 1, $ find the value of $ y"…

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Video Transcript

James Stewart

Calculus: Early Transcendentals

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Kristen Karbon

Michael Jacobsen

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Kayleah Tsai

Caleb Elmore

Kristen Karbon

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Kayleah Tsai

Caleb Elmore

Kristen Karbon

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James Stewart

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