例1 求函数 =(e)^x+2y 的所有二阶偏导数和 dfrac ({a)^3z}(partial ypartial {x)^2}

3.设 =sin (xy)+varphi (x,dfrac (x)(y)), 其中φ(u,v)具有二阶连续偏导数,求 dfrac ({partial )^2z}

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

17.设 =varphi (x+y,(x)^2), 且φ具有二阶连续偏导数,求 dfrac (partial x)(partial x) ,dfrac ({a)

1.求下列函数的高阶偏导数:-|||-(1) =(x)^4+(y)^4-4(x)^2(y)^2 ,所有二阶偏导数;-|||-(2) =(e)^x(cos y+x

(3)已知函数 =f(xy,(e)^x+y) ,且f(x,y)具有二阶连续偏导数.则-|||-dfrac ({partial )^2z}(partial xpa

15.设函数 =f(x+y,(e)^xy), 其中f具有二阶连续偏导数,求 a^2/ax, dfrac ({sigma )^2z}(partial {{x)^2

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}(

[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((x)^3+(y)^2), 其中f具有二阶连续偏导数,则 dfrac ({partial )^2z}(partial {y)^2}=

13.17 设函数 =f(ln sqrt ({x)^2+(y)^2}) 有二阶连续偏导数,满足 dfrac ({partial )^2u}(partial {x