1.设f,φ是C^(2)类类函数, =yf(dfrac (x)(y))+xvarphi (dfrac (y)(x)), 求:(1) a2/ey; (2) dfrac ({partial )^2z}(partial {x)^2}+ydfrac ({partial )^2z}(partial x)

求下列函数的 dfrac ({a)^2z}(a{x)^2} ,dfrac ({partial )^2z}(partial xpartial y) ,dfrac

3.设 =dfrac (y)(f({x)^2-(y)^2)} ,其中f为可微函数,验证-|||-dfrac (1)(x)dfrac (partial z)(pa

7.设 =dfrac (y)(f({x)^2-(y)^2)} 其中f为可导函数,验证: dfrac (1)(x)dfrac (partial z)(partia

dfrac ({sigma )^2z}(partial {y)^2} 和 dfrac ({partial )^2z}(partial xpartial y):-

11.设 =f((x)^2+(y)^2) ,其中f具有二阶导数,求 dfrac ({a)^2z}(d{x)^2} -dfrac ({partial )^2z}(

5.设 sin (x+2y-3z)=x+2y-3z, 证明: dfrac (partial z)(partial x)+dfrac (partial z)(pa

设 =dfrac (y)(f({x)^2-(y)^2)} ,其中f(u)为可导函数,验证-|||-.dfrac (1)(x)dfrac (dz)(partial

[题目]-|||-设变换 ^2)+dfrac ({partial )^2z}(partial xpartial y)-dfrac ({partial )^2

1.已知 sin (3x-2y+z)=3x-2y+z, 则 dfrac ({partial )^2z}(partial xpartial y)= __

[题目]设函数f w)具有二阶连续导数, =f((e)^xcos y)-|||-满足 dfrac ({partial )^2z}(partial {x)^2}+