The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
$2x+y+xy^{\prime}-2y\cdot y^{\prime}=0$
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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
$xy^{\prime}-2y\cdot y^{\prime}=-2x-y$
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Factor the polynomial $xy^{\prime}-2y\cdot y^{\prime}$ by it's greatest common factor (GCF): $y^{\prime}$
Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.