求微分dy是求微分吧,那最后还要加个dx了?

网友回答

y=cos^3(1/x)
y'=3cos^2(1/x)(cos1/x)'
=3cos^2(1/x)[-sin(1/x)](1/x)'
=-3cos^2(1/x)*[-sin(1/x)]*(-1/x^2)
=3cos^2(1/x)*[sin(1/x)]/(x^2)
dy=3cos^2(1/x)*[sin(1/x)]/(x^2)dx
======以下答案可供参考======
供参考答案1:
y=cos^3(1/x)
y'=3cos^2(1/x)(cos1/x)'
=3cos^2(1/x)(-sin1/x)(1/x)'
=-3cos^2(1/x)*sin(1/x)(-1/x^2)
=3cos^2(1/x)sin(1/x)/[x^2)
所以 dy=3cos^2(1/x)sin(1/x)/[x^2]dx
供参考答案2:
y'=3cos(1/x)^2*(-sin(1/x))*(-1/x^2)
= 1.5sin(2/x)cos(1/x)
dy=1.5sin(2/x)cos(1/x)dx
其实就是先对y求导,再加dx