Question

calcule a derivada da função implícita
3x2 -y2/2 =18

Answer 1

$\bold{3x^{2} \ - \ \frac{y^{2}}{2} \ = \ 18}$


Derivando implicitamente:

$2 \ . \ 3x^{(2 \ - \ 1)} \ - \ \frac{2 \ . \ y^{(2 \ - \ 1)} \ . \ y' \ . \ 2 \ - \ (y^2 \ . \ 0)}{2^2} \ = \ 0$

$6x^{1} \ - \ \frac{2y^{1} \ . \ 2y' \ - \ 0}{4} \ = \ 0$

$6x \ - \ \frac{2y \ . \ 2y'}{4} \ = \ 0$

$6x \ - \ \frac{4y.y'}{4} \ = \ 0$

$6x \ - \ \frac{\not{4}y.y'}{\not{4}} \ = \ 0$

$6x \ - \ y.y' \ = \ 0$

$-y.y' \ = \ -6x$

$y' \ = \ \frac{-6x}{-y}$

$\boxed{\bold{y' \ = \ \frac{6x}{y}}}$