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求导数sin xy x y

见图

对x求导是ycos(xy).对y求导是xcos(xy)

∂Z/∂x= y*cos(xy) -2cos(xy)*sin(xy)*y = y*cos(xy) - y*sin(2xy) ∂Z/∂y= x*cos(xy) -2cos(xy)*sin(xy)*x = x*cos(xy) - x*sin(2xy)

两边同时对x求导 e^x-e^yy'=cos(xy)(y+xy') y'=[e^x-ycos(xy)]/【xcos(xy)+e^y】 dy/dx=[e^x-ycos(xy)]/【xcos(xy)+e^y】

函数 f(x,y) = xy/√(x²+y²),(x,y)≠(0,0), = 0, (x,y)=(0,0), 求偏导数 f'x(x,y) = y³/[√(x²+y²)]³,(x,y)≠(0,0), = 0,(x,y)=(0,0), 而因 lim(x→0,y=kx)f'x(x,y) = lim(x→0,y=kx)y³/[√(x²+y²...

题目不明确无法作答

(sin²x)' = 2sinx(sinx)'  = 2sinxcosx  = sin2x 或: (sin²x)' = [(1-cos2x)/2]'  = [1/2 - (cos2x)/2]'  = 0 - ½(-sin2x)(2x)'  = ½(sin2x)×2  = sin2x

等下

sin xy对x进行求导,就把x看作未知数,把y看作常数,sin x求导得到cos x(这时把xy看作一个整体),xy对x求导得到y,刚好两者相乘,得到ycos xy

sin(xy)=x²y²+e^xy, 两边求导得到: cos(xy)(ydx+xdy)=2xy^2dx+2x^2ydy+e^(xy)(ydx+xdy) y[cos(xy)-e^(xy)]dx+x[cos(xy)-e^(xy)]dy=2xy^2dx+2x^2ydy x[cos(xy)-e^(xy)-2xy]dy=y[2xy-cos(xy)+e^(xy)]dx 所以: dy/dx=y[2xy-cos(xy)+e^(...

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