Question

производная неявной функции
(y^2)/4-(x^2)/9=1
Найти y'(0)

Answer 1

$(\frac{ {y}^{2} }{4})' \: - (\frac{ {x}^{2} }{9})'= (1)' \\ \frac{2y}{4} y' - \frac{2x}{9} = 0 \\y' = \frac{2x}{9} \div \frac{y}{2} \\ y' = \frac{4x}{9y} \\ y'(0) = \frac{4 \times 0}{9y} = 0$