Геометрический смысл производной

y_{k} = f^{'} (a) (x - a) + f (a)

y_{n} = - \frac{1}{f ^{'} ( a )} (x - a) + f (a)

$y = arccos 3 x y_{k} - ? y_{n} = ?$

y_{k} = y^{'} (a) (x - a) + y (a) y_{n} = - \frac{1}{y ^{'} ( a )} (x - a) + y (a)

a = 0; y (0) = \frac{π}{2}; y^{'} = (arccos 3 x)^{'} = - \frac{1}{1 - 9 x ^{2}}; y^{'} (0) = - 3

y_{k} = y^{'} (t_{0}) (x - x_{0}) + y (t_{0}) y_{n} = - \frac{1}{y ^{'} ( t _{0} )} (x - x_{0}) + y (t_{0}) 23 = 4 cos t_{0} cos t_{0} = \frac{3}{2} t_{0} = \pm \frac{π}{6} + 2 πk; k \in Z y (t_{0}) = {1, 5; При t_{0} = \frac{π}{6} + 2 πk; k \in Z - 1, 5; При t_{0} = - \frac{π}{6} + 2 πk; k \in Z {y_{x}^{'} = \frac{3 c o s t}{- 4 s i n t} x = 4 cos t {y_{x}^{'} = - 0, 75 cot t x = 4 cos t y_{x}^{'} (t_{0}) = {- 0, 753; При t_{0} = \frac{π}{6} + 2 πk; k \in Z 0, 753; При t_{0} = - \frac{π}{6} + 2 πk; k \in Z A (23, 1.5); B (23, - 1.5)

y_{k} = y^{'} (x_{0}, y_{0}) (x - x_{0}) + y_{0} y_{n} = - \frac{1}{y ^{'} ( x _{0} , y _{0} )} (x - a) + f (a)