Final Answer
Step-by-step Solution
Specify the solving method
Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable
The derivative of the constant function ($1$) is equal to zero
The derivative of a sum of two or more functions is the sum of the derivatives of each function
The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=y$
The derivative of the linear function is equal to $1$
The derivative of the linear function is equal to $1$
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
The derivative of the linear function is equal to $1$
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
Group the terms of the equation by moving the terms that have the variable $y^{\prime}$ to the left side, and those that do not have it to the right side
Factor the polynomial $xy^{\prime}-2y\cdot y^{\prime}$ by it's greatest common factor (GCF): $y^{\prime}$
Divide both sides of the equation by $x-2y$
Simplifying the quotients