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$5-20$ Find dy/dx by implicit differentiation.$$2 x^{3}+x^{2} y-x y^{3}=2$$

$\frac{y^{3}-2 x y-6 x^{2}}{\left(x-3 y^{2}\right) x}$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Differentiation

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In mathematics, precalculu…

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Find $ dy/dx $ by implicit…

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Implicit differentiation U…

this probably won't use implicit differentiation to find a group of a two X. Youtube plus X squared Y minus X. Y cubed Is equal to two. And so in order to find a derivative here where you don't use implicit differentiation. Now the groove to execute is six X squared. Now for the driver of expert why we need to use the product rule. The derivative of X squared is to actually have two X. Times. Why plus the derivative of Y. Is why crime times X. Word. And then now I need the derivative of X. Y cube. The derivative of X. Is one. Mhm. And the drought of white cube is three Y squared by prime. And then we have times yet he put the white cube. Keep would have white crimes in them on the same side. And then pull why prime out? This is why prime times X squared -3 X. Y. Squared. I'm sorry Southside zero. The directive of 20. Yeah I know it's zero and then take everything else over to the other side. So it'll change signs so it's negative six X. Word minus two. Xy plus. Why cute? Mhm. And then divide everything by X squared -3 X. Watchword. And so this gives us why prime does negative six X squared minus two. Xy. Close Y cubed over. That's weird minus three X Y squared. That's what you're in.

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