Question

derivada implicita de 3(x^2+y^2)^2=100xy?

Answer 1

$3\,(x^{2}+y^{2})=100\,xy$


Derivando implicitamente os dois lados, em relação a $x,$ temos

$\dfrac{d}{dx}\,[3\,(x^{2}+y^{2})]=\dfrac{d}{dx}(100\,xy)\\ \\ \\ 3\,\dfrac{d}{dx}\,(x^{2}+y^{2})=100\,\dfrac{d}{dx}\,(xy)\\ \\ \\ 3 \left[\dfrac{d}{dx}\,(2x)\cdot y^{2}+x^{2}\cdot \dfrac{d}{dx}\,(y^{2}) \right ]=100 \left[\dfrac{d}{dx}\,(x)\cdot y+x\cdot \dfrac{d}{dx}\,(y) \right ]\\ \\ \\ 3 \left[2\cdot y^{2}+x^{2}\cdot 2y\cdot \dfrac{dy}{dx} \right ]=100 \left[1\cdot y+x\cdot \dfrac{dy}{dx} \right ]\\ \\ \\ 3 \left[2y^{2}+2x^{2}\,y\cdot \dfrac{dy}{dx} \right ]=100 \left[y+x\cdot \dfrac{dy}{dx} \right ]$