tangent x/y =sin((pixy)/2),(1,1)

解答

切线

\frac{x}{y} = sin (\frac{π x y}{2}), (1, 1)

y = x

求解步骤

计算

\frac{x}{y} = sin (\frac{π x y}{2})

的斜率:

\frac{d y}{d x} = - \frac{π y ^{3} cos ( \frac{π x y}{2} ) - 2 y}{x ( 2 + π y ^{2} cos ( \frac{π x y}{2} ) )}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 1

找到斜率 m=

1

且穿过

(1, 1)

的直线:

y = x

y = x

\frac{\partial}{\partial x} (y^{2} + 2 x y - x^{2})

x \to 16 lim (x + 2 x)

d er i v a t i v e y = x \cdot x

t an g e n t y = 4 x - 3 x^{2} (2 - 4)

3 x y^{3} d x - (x + 2) d y = 0