Question

y=根号下cosx,求y^(4)的导数

Answer 1

y = √cosx
y² = cosx
2yy' = - sinx..............................................y' = -sinx / 2y
yy' = -0.5 sinx
y'² + yy'' = -0.5 cosx.................................y'' = -(y'² + 0.5cosx)/y
2y'y'' + y'y'' + yy''' = 0.5 sinx
3y'y'' + yy''' = 0.5 sinx..............................y''' = (0.5sinx-3y'y'')/y
3(y''y''+y'y''') + y'y'''+yy'''' = 0.5cosx
y'''' = (0.5cosx - 3y''² - 4y'y''')/y................(★)
依次将：y，y'，y''，y'''，代入(★) 式即为所求：y(⁴)。
这一步请您自己做啦。