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Implicit diffrention problems I am really stuck on

Implicit diffrention problems I am really stuck on-example-1
User WiSaGaN
by
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1 Answer

4 votes

Answer:


(dy)/(dx) =(4x^3+3x^2y-5y^2)/(10xy-3y^2-x^3)

Explanation:

solving for dy/dx

multiply the equation out to remove parentheses


x^4 + x^3y = 5xy^2 -y^3

now differentiating in terms of x (
(dy)/(dx))


4x^3 +3x^2y + x^3((dy)/(dx) ) = 5y^2 + 10xy((dy)/(dx) )-3y^2((dy)/(dx) )

isolating dy/dx to one side


4x^3 +3x^2y - 5y^2= 10xy((dy)/(dx) )-3y^2((dy)/(dx) )-x^3((dy)/(dx) )


4x^3 +3x^2y - 5y^2= (dy)/(dx)(10xy-3y^2-x^3)


(dy)/(dx) =(4x^3+3x^2y-5y^2)/(10xy-3y^2-x^3)

User Arpit Rawat
by
8.3k points

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