求f(x)=x-sin(x/2)cos(x/2)的导数
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求f(x)=x-sin(x/2)cos(x/2)的导数求f(x)=x-sin(x/2)cos(x/2)的导数求f(x)=x-sin(x/2)cos(x/2)的导数f(x)*f(y)的导数是f(x)的导
求f(x)=x-sin(x/2)cos(x/2)的导数
求f(x)=x-sin(x/2)cos(x/2)的导数
求f(x)=x-sin(x/2)cos(x/2)的导数
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)
f(x)的导数=1-[(1/2)cos(x/2)cos(x/2)-(1/2)sin(x/2)sin(x/2)]
=1-(1/2)cos(x)
1-0.5*cosx
因为sin2x=2sinxcosx
所以
f(x)=x-1/2sinx
f(x)导数=1-1/2cosx
1-1/2[cos(x/2)cos(x/2)-sin(x/2)sin(x/2)]=1-0.5cosx
1-1/2*cos(x/2)^2+1/2*sin(x/2)^2
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