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  • 4 years ago

given an implicit function y+xy+y ^{2}=2 how do you find its derivative..

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  1. ash2326
    • 4 years ago
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    Find the derivative with respect to x for each term, I'll show you we need to find dy/dx \[\frac{d}{dx}( y+xy+ y^2)=\frac{d}{dx} (2)\] we get \[\frac{dy}{dx}+y+x\frac{dy}{dx}+2y\frac{dy}{dx}=0\] now combine common terms \[\frac{dy}{dx}(1+x+2y)+y=0\] \[=> \frac{dy}{dx}(1+x+2y)=-y\] so we get \[\frac{dy}{dx}=-\frac{y}{1+x+2y}\] The point to remember is to combine all dy/dx terms and then find dy/dx

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