✔ 最佳答案
1a)a = (1-2x)/(1+2x)
da / dx = { ( 1 + 2x ) d / dx ( 1 – 2x ) – ( 1 – 2x ) d / dx ( 1 + 2x ) } / ( 1 + 2x )2
= { ( 1 + 2x )( - 2 ) – ( 1 – 2x )( 2 ) } / ( 1 + 2x )2
= ( - 2 – 4x – 2 + 4x ) / ( 1 + 2x )2
= -4 / ( 1 + 2x )2
b)y2 = sec a
y = ( sec a )1/2
dy / da = ( 1 / 2 )( sec a )-1/2 ( sec a )( tan a )
= ( 1 / 2 )( sec a )1/2 ( tan a )
( da / dx )( dy / da ) = dy / dx
dy / dx = {( 1 / 2 )( sec a )1/2 ( tan a )}{ -4 / ( 1 + 2x )2 }
= - 2( sec a )1/2 ( tan a ) / ( 1 + 2x )2
( 1 + a )2 = ( 1 + ( 1 – 2x ) / ( 1 + 2x ) )2
= ( 1 + 2x + 1 – 2x )2 / ( 1 + 2x )2
= 4 / ( 1 + 2x )2
Therefore,
dy / dx = - 2( sec a )1/2 ( tan a ) / ( 1 + 2x )2
= - ( 1 / 2 )( 1 + a )2( sec a )1/2 ( tan a )
x = y + sin y
dx / dy = 1 + cos y
1 / dx / dy = 1 / ( 1 + cos y )
dy / dx = ( 1 + cos y )-1
d2y / dx2 = - ( 1 + cos y )-2 ( - sin y )
= sin y ( 1 + cos y )-2
( Something wrong with this answer )
