Question

Implicit diffrention problems I am really stuck on

Answer 1

`(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)`