Question

Implicit diffrention problems I am really stuck on

Answer 1

Answer:

$\frac{dy}{dx} =\frac{4x^3+3x^2y-5y^2}{10xy-3y^2-x^3}$

Step-by-step 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 ($\frac{dy}{dx}$)

$4x^3 +3x^2y + x^3(\frac{dy}{dx} ) = 5y^2 + 10xy(\frac{dy}{dx} )-3y^2(\frac{dy}{dx} )$

isolating dy/dx to one side

$4x^3 +3x^2y - 5y^2= 10xy(\frac{dy}{dx} )-3y^2(\frac{dy}{dx} )-x^3(\frac{dy}{dx} )$

$4x^3 +3x^2y - 5y^2= \frac{dy}{dx}(10xy-3y^2-x^3)$

$\frac{dy}{dx} =\frac{4x^3+3x^2y-5y^2}{10xy-3y^2-x^3}$