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f(1,2)=4,df(1,2)=16dx+4dy,df(1,4)=64dx+8dy,则z=f(x,f(x,y))在点（1,2）出对x的偏导数是多少?
题目详情
f(1,2)=4,df(1,2)=16dx+4dy,df(1,4)=64dx+8dy,则z=f(x,f(x,y))在点（1,2）出对x的偏导数是多少?
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答案和解析
partial_f(1,2)/partial_x=16
partial_f(1,4)/partial_x=64
partial_f(1,4)/partial_y=8
dz/dx=partial_f(x,f(x,y))/partial_x+partial_f(x,f(x,y))/partial_f(x,y) * parital_f(x,y)/partial_x
代入（1,2）坐标,有
f(x,f(x,y))=f(1,4)
dz/dx=partial_f(x,f(x,y))/partial_x+partial_f(x,f(x,y))/partial_f(x,y) * parital_f(x,y)/partial_x
=64+8 * 16
=192
partial_f(1,4)/partial_x=64
partial_f(1,4)/partial_y=8
dz/dx=partial_f(x,f(x,y))/partial_x+partial_f(x,f(x,y))/partial_f(x,y) * parital_f(x,y)/partial_x
代入（1,2）坐标,有
f(x,f(x,y))=f(1,4)
dz/dx=partial_f(x,f(x,y))/partial_x+partial_f(x,f(x,y))/partial_f(x,y) * parital_f(x,y)/partial_x
=64+8 * 16
=192
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