Question

Utilizando a derivação implícita, podemos afirmar que a derivada da função implícita    5x-x2y3=2y  é:​

Answer 1

$\large\boxed{\begin{array}{l}\rm Utilizando\,a\,derivac_{\!\!,}\tilde ao\,impl\acute icita,podemos\,afirmar\\\rm que\,a\,derivada\,da\,func_{\!\!,}\tilde ao\,impl\acute icita\\\rm 5x-x^2y^3=2y\,\acute e:\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\boldsymbol{soluc_{\!\!,}\tilde ao\!:}}\\\sf 5x-x^2y^3=2y\\\sf 5-\bigg(2xy^3+x^2\cdot3y^2\cdot\dfrac{dy}{dx}\bigg)=2\dfrac{dy}{dx}\\\\\sf 5-2xy^3-3x^2y^2\dfrac{dy}{dx}=2\dfrac{dy}{dx}\\\\\sf -3x^2y^2\dfrac{dy}{dx}-2\dfrac{dy}{dx}=2xy^3-5\cdot(-1)\\\\\sf 3x^2y^2\dfrac{dy}{dx}+2\dfrac{dy}{dx}=5-2xy^3\\\\\sf\dfrac{dy}{dx}\cdot(3x^2y^2+2)=5-2xy^3\\\huge\boxed{\boxed{\boxed{\boxed{\sf \dfrac{dy}{dx}=\dfrac{5-2xy^3}{3x^2y^2+2}}}}}\end{array}}$