implicit derivative of (dy)/(dx),y^2(y^2-4)=x^2(x^2-5)

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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implicit derivative dydx , y²(y²−4)=x²(x²−5)

Solution

dydx =x(2x²−5)2y(y²−2)

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y²(y²−4)=x²(x²−5)

Treat y as y(x)

Differentiate both sides: 4y³dydx −8ydydx =4x³−10x

Isolate dydx : dydx =x(2x²−5)2y(y²−2)

dydx =x(2x²−5)2y(y²−2)

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implicit derivative of (dy)/(dx),y^2(y^2-4)=x^2(x^2-5)

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