Question

高中:求 f(x)= [ cos(Inx) ] ^2 的导数

请写一下详细过程.谢谢

Answer 1

这是复合函数，
f(x)=x^2
g(x)=cosx
h(x)=lnx
所以f{g[h(x)]}=[ cos(Inx) ] ^2
所以首先对平方求导，再对cos求导，最后对ln求导
所以f'(x)=2cos(lnx)*[cos(lnx)]'
=2cos(lnx)*[-sin(lnx)]*(lnx)'
=2cos(lnx)*[-sin(lnx)]*(1/x)
=-2cos(lnx)*sin(lnx)*(1/x)
=-[sin(2lnx)]/x

Answer 2

f'(x)=-sin(2lnx)/x

Answer 3

2cos(lnx)*(-sin(lnx))*(1/x)

Answer 4

f(x)= [ cos(Inx) ] ^2
f'(x)= 2*[ cos(Inx) ] * [cos(Inx)]'
其中：[cos(Inx)]'
＝-sin(Inx)*(Inx)'
=-sin(Inx)*1/x
所以f'(x)= 2*[ cos(Inx) ] *（-sin(Inx)*1/x）
＝－2*cos(Inx)*sin(Inx)/x=-sin(2lnx)/x

Answer 5

解：f‘(x)= 2[ cos(Inx) ] * [ cos(Inx) ] ’
=2[ cos(Inx) ] * [ sin(Inx) ] *(Inx)‘
=2[ cos(Inx) ] * [ sin(Inx) ] /x
=2sin(2lnx)/x

Answer 6

f(x)*f(y)的导数是
f(x)的导数乘以f(y)+f(x)乘以f(y)的导数
所以f(x)的导数是
1-(1/2*cos(x/2)*cos(x/2)+sin(x/2)*(-sin(x/2))*1/2)
=1-(1/2*cos(x/2)^2-1/2sin(x/2)^2)
=1-1/2(cos(x/2)^2-sin(x/2)^2)
cosa^2-sina^2=cos2a
=1-1/2cos(x)