[tex]f(x,y,z)=xy+yz+zx[/tex]
[tex]\implies\nabla f(x,y,z)=(y+z,x+z,y+x)[/tex]
[tex]\vec{pq}=\mathbf q-\mathbf p=(2-1,4-(-1),5-7)=(1,5,-2)[/tex]
[tex]\|\vec{pq}\|=\sqrt{30}[/tex]
[tex]D_{\vec{pq}}f(1,-1,7)=\nabla f(1,-1,7)\cdot\dfrac{(1,5,-2)}{\sqrt{30}}=\dfrac{(6,8,0)\cdot(1,5,-2)}{\sqrt{30}}=\dfrac{46}{\sqrt{30}}[/tex]
