y=x^2sin1/x的导数是什么
问题描述：
y=x^2sin1/x的导数是什么
答
y=x^2.sin(1/x)
y' = x^2 cos(1/x) . ( -1/x^2) + 2xsin(1/x)
= -cos(1/x) +2xsin(1/x)还是看不明白。为什么要加(uv)' = uv' + vu'y =x^2 sin(1/x) = x^2 [ sin(1/x) ] ' + sin(1/x) . (x^2)' = x^2 (cos(1/x) ) . (1/x)' +sin(1/x) . (2x)= x^2 (cos(1/x) ) .(-1/x^2) + 2xsin(1/x) = -cos(1/x) + 2xsin(1/x)