大一高数 导数

大一高数 导数求手写
2025-12-25 10:58:55
推荐回答(1个)
回答1:

2. x^2/a^2 + y^2/b^2 = 1, 两边对 x 求导, 得
2x/a^2 + 2yy'/b^2 = 1, y' = -xb^2/(ya^2)
在 P(a/√2, b/√2) y' = -b/a, 法线斜率 k = a/b,
Ox 轴到内法线得转角 t = π+arctan(a/b)
z = 1-(x^2/a^2+y^2/b^2),
z' = -2x/a^2, z'(P) = -√2/a
z' = -2y/b^2, z'(P) = -√2/b
∂z/∂L = cost z' + sint z'
= (-√2/a)[-a/√(a^2+b^)] + (-√2/b)[-b√(a^2+b^)]
= 2√2/√(a^2+b^)