Question

qual a derivação implicita x²y²+xseny=4​

Answer 1

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$\sf x^2+y^2+xsen(y)=4\\\sf 2x+2y\dfrac{dy}{dx}+sen(y)+xcos(y)\dfrac{dy}{dx}=0\\\sf 2y\dfrac{dy}{dx}+xcos(y)\dfrac{dy}{dx}=-2x-sen(y)\\\sf\dfrac{dy}{dx}(2y+xcos(y))=-2x-sen(y)\\\huge\boxed{\boxed{\boxed{\boxed{\sf \dfrac{dy}{dx}=-\dfrac{2x+sen(y)}{2y+xcos(y)}}}}}$