求解一道高数题,要详细过程,谢谢!!!!

2024-11-06 02:55:18
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回答1:

方程z=f(x,y)两边对激岩橡x求偏导,注意此时把z看做自变枣灶量,y看出x,z的函数,得0=f1+f2*ðy/ðx,则 ðy/ð明旁x=-f1/f2,所以ð^2y/ðx^2=-[f2(f11+f12*ðy/ðx)-f1(f21+f22*ðy/ðx)]/(f2)^2=[f21f1-f11f2+(f22f1-f12f2)ðy/ðx]/(f2)^2=(f21f1=f11f2-f22f1f1/f2+f12f1)/(f2)^2=[f21f1f2-f11(f2)^2-f22(f1)^2+f12f1f2]/(f2)^3=0