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举ä¾åå¦ä¸ï¼ç¨æéå®ä¹æ±å½æ°z=x^2+xy+y^2çä¸é¶å导æ°z'xãz'yçå
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z'x
=lim(tâ0)[(x+t)^2+(x+t)y+y^2-(x^2+xy+y^2)]/t,
=lim(tâ0)[2xt+t^2+(x+t)y-xy)]/t,
=lim(tâ0)[2xt+t^2+ty)]/t,
=lim(tâ0)(2x+t+y)
=2x+yã
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z'y
=lim(tâ0)[x^2+x(y+t)+(y+t)^2-(x^2+xy+y^2)]/t,
=lim(tâ0)(xt+2ty+t^2)/t,
=lim(tâ0)(x+2y+t),
=x+2yã
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