设向量场A(x，y，z)=y2i+ezj+ln(1+z2)k，r=xi+yj+zk，则grad(A•r)=____．

设向量场A(x，y，z)=y²i+e^zj+ln(1+z²)k，r=xi+yj+zk，则grad(A•r)=____．
【正确答案】：y²i+(2xy+e²)j+[e^zy+ln(1+z²)+2z² /(1+z²)]k. 解析：grad(A•r)=( ∂A•r/∂x)i+(∂A•r/∂y)j+(∂A•r/∂z)ky²i+(2xy+e ²)j+[e^zy+ln(1+z²)+2z²/(1+z²)]k