设z=f(x,y)在(2,2)可微,f(2,2)=2,f对x的偏导在(2,2)等于1,f对y的偏导在(2,2)等于3,u(x)=f(x,f(x,x))求u(x)^2对x的全导数在(2,2)处的值.

Question

设z=f(x,y)在(2,2)可微,f(2,2)=2,f对x的偏导在(2,2)等于1,f对y的偏导在(2,2)等于3,u(x)=f(x,f(x,x))
求u(x)^2对x的全导数在(2,2)处的值.

Answer 1

注：f 后面的1,2表示下标设w=u²(x),dw/dx=2u(x)*u'(x)u'(x)=f1'+f2'*(f1'+f2')=f1'+f1'f2'+(f2')²将x=2代入得：u'(2)=f1'(2,2)+f1'(2,2)f2'(2,2)+(f2'(2,2))²=1+1*3+3²=13dw/dx在x=2的值为：2u(...