y=xsin^2 x求导 求导数，y＝sin^2X

Y=xsin(x^2+1)\u7684\u5bfc\u6570

Let u=x^2+1, du/dx = 2x
dsinu/du=cosu,
dsin(x^2+1)/dx = 2x*cosu = 2xcos(x^2+1)

dy/dx = sin(x^2+1) + x*2xcos(x^2+1) = sin(x^2+1) + 2x^2 cos(x^2+1)

(sin²x)' = 2sinx(sinx)' 
= 2sinxcosx 
= sin2x
\u6216\uff1a
(sin²x)' = [(1-cos2x)/2]' 
= [1/2 - (cos2x)/2]' 
= 0 - ½(-sin2x)(2x)' 
= ½(sin2x)\u00d72 
= sin2x

y=xsin^2 x
u=x u'=1
v=sin²x v'=2sinxcosx

所以
y'=u'v+uv'
=sin²x+2xsinxcosx

y=xsin²x
y′=sin²x+2xsinxcosx
=sin²x+xsin2x

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