Question

y=cos^2(x^2+1)求导，要详细过程，运用什么方法

Answer 1

y′=2cos^2(x^2+1)(-sin(x^2+1))·2x=-2xsin(2x^2+2)
先将cos^2(x^2+1)看成整体即为cos^2t,求导的：2cost·(-sint),而t=x^2+1,
求导的：2x,
综上：y′=-2xsin(2x^2+2)

Answer 2

y'=[cos^2(x^2+1)]'
=[2cos(x^2+1)]·[cos(x^2+1)]'
=[2cos(x^2+1)]·[-sin(x^2+1)]·[x^2+1]'
=[2cos(x^2+1)]·[-sin(x^2+1)]·2x
中间用的都是链导法则

Answer 3

解：y'=[cos²(x²+1)]'
=2cos(x²+1)*[cos²(x²+1)]'
=-2cos(x²+1)*sin(x²+1)*(x²+1)'
=-4xcos(x²+1)*sin(x²+1)
=-2xsin[2(x²+1)]。

Answer 4

解：y‘=2cos（x^2+1）*sin(x^2+1)*2x
=2x*sin[2*（x^2+1）]

Answer 5

y' = ( cos^2(x^2 + 1) )'
= 2*cos(x^2 + 1) * (cos(x^2 + 1))'
= 2^cos(x^2 + 1) * (-sin(x^2 + 1)) * (x^2 + 1)'
= 2^cos(x^2 + 1) * (-sin(x^2 + 1)) * 2x
= -4x*cos(x^2 + 1) * sin(x^2 + 1)