f(x,y,z)=sin(xy)cos(yz)的二阶偏导数怎么求

1.先求一阶偏导,比如对x求一阶偏导,对x求偏导数就把y和z视为常数,结果为sin(xy)'(xy)'cos(yz)+sin(xy)cos(yz)'(yz)'=cos(xy)*y*cos(yz)-sin(xy)*sin(yz)*0=cos(xy)*y*cos(yz) //注意(xy)' 对x求偏导时结果为y,因为此时y为常数.然后再对y,z求偏导,原理是一样的.
2.再求2阶偏导,比如对x求2阶偏导数,即将x的一阶偏导结果cos(xy)*y*cos(yz)再对x求一次偏导,原理还是一样的,将y和z视为常数.