求下列函数的 dfrac ({a)^2z}(a{x)^2} ,dfrac ({partial )^2z}(partial xpartial y) ,dfrac ({a)^2z}(a{y)^2} (其中f具有二阶连续偏导数):-|||-(1) z=f(xy,y) ;-|||-(2) =f(x,dfrac (x)(y)) ;-|||-(3) =f(x(y)^2,(x)^2y) ;-|||-(4) =f(sin x,cos y,(e)^x+y) .

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

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}(

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

6.设 ^3-2xz+y=0, 求 a^2z/ax^2, dfrac ({a)^2z}(partial {y)^2}.

[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}+

设f具有二阶连续偏导数, =xf(x,dfrac (y)(x)), 求 dfrac ({partial )^2z}(partial xpartial y)

若z=f(x,y),x=u+v,y=u-v,则(partial^2z)/(partial upartial v)=(partial^2z)/(partial x

设函数 z=z(x,y) 由方程 ^3-3xyz=8 确定,求 dfrac ({a)^2z}(a{x)^2partial y}(|)_(x-a)

33.设函数 z=z(x,y) 由方程 +x=(e)^z-y 所确定,则 dfrac ({partial )^2z}(partial ypartial x)=