find-grad-r-m-where-r-x-2-y-2-z-2-

Question Number 84624 by subhankar10 last updated on 14/Mar/20

find grad r^{m} where r = x^{2} + y^{2} + z^{2}

Answered by TANMAY PANACEA last updated on 14/Mar/20

\vec{▽} = i \frac{\partial}{\partial x} + j \frac{\partial}{\partial y} + k \frac{\partial}{\partial z} i s g r a d e

t o f i n d \vec{▽} {(x^{2} + y^{2} + z^{2})}^{m}

(i \frac{\partial}{\partial x} + j \frac{\partial}{\partial y} + k \frac{\partial}{\partial z}) {(x^{2} + y^{2} + z^{2})}^{m}

= m {(x^{2} + y^{2} + z^{2})}^{m - 1} (i 2 x + j 2 y + k 2 z)

= {m r}^{m - 1} \times 2 (\vec{r}) = 2 {m r}^{m - 1} . \vec{r}

o r m {(x^{2} + y^{2} + z^{2})}^{m - 1} \times 2 (i x + j y + k z)

Commented by subhankar10 last updated on 15/Mar/20

thank you sir

Commented by TANMAY PANACEA last updated on 15/Mar/20

m o s t w e l c o m e