y=sin^2 {x/(x+1)} 求dy
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y=sin^2{x/(x+1)}求dyy=sin^2{x/(x+1)}求dyy=sin^2{x/(x+1)}求dydy=2sin[x(x+1)]cos[x(x+1)](2x+1)dy=2sin[x/(
y=sin^2 {x/(x+1)} 求dy
y=sin^2 {x/(x+1)} 求dy
y=sin^2 {x/(x+1)} 求dy
dy=2sin[x(x+1)]cos[x(x+1)](2x+1)
dy=2sin[x/(x+1)]cos[x/(x+1)]/(x+1)^2
设 x/(x+1)=u则y=sin²u
因此,
dy/dx=(dy/du)*(du/dx)
其中,
dy/du=2sinucosu;du/dx=(x+1-x)/(x+1)²=1/(x+1)²
解得:
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设 x/(x+1)=u则y=sin²u
因此,
dy/dx=(dy/du)*(du/dx)
其中,
dy/du=2sinucosu;du/dx=(x+1-x)/(x+1)²=1/(x+1)²
解得:
dy=(dy/du)*(du/dx)
=2sinucosu*1/(x+1)²
=2sin {x/(x+1)} cos {x/(x+1)}/(x+1)²
这种题目做熟悉了之后,连上面的步骤都不需要写,可以直接写出答案。
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