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Use implicit differentiation to find an equation …

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Problem 26 Easy Difficulty

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
$ \sin (x + y) = 2x - 2y, (\pi, \pi) $

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September 30, 2020

what kind of explanation is this Frank. You did the math in your in head. Thanks for help scumbag.

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Video Transcript

In this problem were given a cur and we are students differentiation to find the equation of the tangent line at a given .55 to sure. We know that the equation of tangent line will be able to form y minus y, not times the arato of this function and will let that the given point x not times x, minus x, not where this is y, not- and this point is x now. So let's say derivative on both sides with respect to x and we have cosine x plus y times. Derivative of inner function to d d x of x plus y is equal to 2 minus 2 y prime, that is cosine x plus y times y prime plus 1 is equal to 2 minus 2 y prime. Let'S group, all the terms with y prime on 1 side, we have y prime 2 plus cosine x, plus y is equal to 2 minus cosine x plus y from this we can see that y prime is 2 minus cosine x, plus y divided by 2 plus Cosine x, plus y and multiply given x not, and i noted, tidy 5 prime. We see that y prime is equal to 2 minus cosine 2 pi divided by 2 plus cosine 2 pi. That is equal to 1 over 3. Now, let's apply everything into the equation of tangent land. We have y minus pi is equal to 1 third x minus pi from the speed and see that equation of tenentes 1 third of x, plus 2 pi over 3.

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