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

## $$y^{\prime \prime}=1 /\left(e^{2}\right)$$

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

this problem were given any question And where's my secondary toe? Why would suspect X clinics is here? So let's first place exterior and and let's see the value hope it function while we're next. Zero. So we have zero times. Why? Plus Egypt A Y is able to be this term is Europe. So from this we see that when x zero y is equal to one All right now fighting for Sarah to have less differentiate bolts X we have why plus X y plane plus each other. Why times y prime music. Zero firmness. We see that Then why Prime is equal tornado You wanted eggs plus each wine What x zero We found that wise a good one less evil 80 the average of at that point. So why prime would then be the originator of one or were zero plus one and that every negative would over eat? All right, now, using this white prime this equation, we're gonna depreciate it there one more time to find secondary tive will use caution. Trolls are white devil would be equal to the negative off. Why prime that was X plus each other. Why plus y times one Waas eating. Why find more prime divided by X plus each other? Why, it's Kurt or it now, Unless you let why? Double prime secondary Quiet one x zero. That is negative. We found why Prime is a coordinated he so we haven't already. Times 01 e plus one times one waas e conflicto e You added by zero plus c squared that these four cancel out. This would cancel out and we didn't find one double time to be negative off negative walk over the script for the answer is one over the square.

#### Topics

Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp