关于高等数学求导的三道小题,求解1,y=arctan(e^√x)(括号里面的是e的根号x次方)2,y=√(1-sin2x/1+sin2x)3,y=arctan[1/2tan(2/x)]谢谢只是求导，不是微分哦

Question

关于高等数学求导的三道小题,求解
1,y=arctan(e^√x) (括号里面的是e的根号x次方)
2,y=√(1-sin2x/1+sin2x)
3,y=arctan[1/2tan(2/x)]
谢谢
只是求导，不是微分哦

Answer 1

1. 令 u = e^√x , u ' = e^√x * 1/(2√x)
y ' = 1/[1+ u²] * u‘ = 1 / [1+ e^(2√x)] * e^√x * 1/(2√x)
2. 令 u = (1- sin2x) / (1+sin2x) = -1 + 2/(1+sin2x),
u ' = -2 / (1+sin2x)² * 2cos2x
y ' = 1/ (2√u) * u ' = 1/ [2√(1- sin2x) / (1+sin2x) ] * (- 4 cos2x) / (1+sin2x)²
3. 令 u = 1/2 tan(2/x) = (1/2) cot(x/2), u ' = (1/2) (-1/2) csc²(x/2)
y ' = 1/[1+ u²] * u‘ = 1 / [ 1+ (1/4) tan²(2/x) ] * (-1/4) csc²(x/2)