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Problem 23 Easy Difficulty

Regard $ y $ as the independent variable and $ x $ as the dependent variable and use implicit differentiation to find $ dx/dy. $
$ x^4y^2 - x^3y +2xy^3 = 0 $

Answer

$$x^{\prime}=\frac{d x}{d y}=\frac{-2 x^{4} y+x^{3}-6 x y^{2}}{4 x^{3} y^{2}-3 x^{2} y+2 y^{3}}$$

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Video Transcript

this problem or winning equation, whereas to find Derek off exits. Why? Since wise independent for your one exit. And so we're gonna think there was a lot of friends with respect. Why was to that organist for a group or the terms, actually, So for excuse, um, y squared the X t one plus two eggs and board. Why, This is their first time with the left hand side minus. We have three expert boy terms t x t war minus excuse. This is their second door on the left. Inside plus to one cute t x t y. I was, um we have six extra reward squared. That is zero. And this was two terms. Is be Derek off the factor with left inside. So now let's group over terms with the x t y. Or be left and senselessly bolster my left inside. We have or excuse Why spread minds three experience. Boy wants to work. You painless, uh, group all the terms we got the FBI or wife inside we have ex uhm cube minus six times X voice cried my street exit for a while and from the species that he ext you are is people to excuse my six x points for a minus two extra for a while you wanted by four Execute one spread minus three x spread boy plus two one.

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