find-grad-log-r-

Question Number 55816 by Rio Mike last updated on 04/Mar/19

f i n d g r a d l o g ∣ r ∣

Answered by tanmay.chaudhury50@gmail.com last updated on 04/Mar/19

g r a d e l n ∣ r ∣

\vec{▽} = (i \frac{\partial}{d x} + j \frac{\partial}{\partial y} + k \frac{\partial}{\partial z}) (l n \sqrt{x^{2} + y^{2} + z^{2}})

= \frac{1}{2} i \frac{\partial}{\partial x} (l n (x^{2} + y^{2} + z^{2}) + \frac{1}{2} j \frac{\partial}{\partial y} ({l n (x^{2} + y^{2} + z^{2})} +

\frac{1}{2} k \frac{\partial}{\partial z} {l n (x^{2} + y^{2} + z^{2})}

= \frac{1}{2} [\frac{2 x}{x^{2} + y^{2} + z^{2}} \times i + \frac{2 y j}{x^{2} + y^{2} + z^{2}} + \frac{2 z k}{x^{2} + y^{2} + z^{z}}]

= \frac{i x + j y + k z}{x^{2} + y^{2} + z^{2}}

= \frac{\vec{r}}{∣ r ∣^{2}}

Commented by otchereabdullai@gmail.com last updated on 04/Mar/19

wow! this is fantastic Prof chaudhury