gradient

Let φ be a scalar function. Then, ∇φ is

The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j})$ is _______ (Rounded off to 1 decimal pla...

Let $f(.)$ be a twice differentiable function from $ \mathbb{R}^{2} \rightarrow \mathbb{R}$. If $P, \mathbf{x}_{0} \in \mathbb{R}^{2}$ where $\vert \vert P\vert \vert$ is sufficien...

Given a function $\rm ϕ = \frac{1}{2} (x^2 + y^2 + z^2) $ in three-dimensional Cartesian space, the value of the surface integral ∯ S n̂ . ∇ϕ dS where S is the surface of a sphere...

For a position vector $\vec{r} = x\hat{i}+y\hat{j}+z\hat{k}$ the norm of the vector can be defined as $|\vec{r}| = \sqrt{x^2 + y^2 + z^2}$. Given a function $\phi = \ln|\vec{r}|$,...

For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }},0} \right)$$ is given by

The directional derivative of the scalar function $$f(x, y, z)$$$$ = {x^2} + 2{y^2} + z\,\,$$ at the point $$P = \left( {1,1,2} \right)$$ in the direction of the vector $$\,\overri...

The expression curl $$\left( {grad\,f} \right)$$ where $$f$$ is a scalar function is

If $$\overrightarrow V $$ is a differentiable vector function and $$f$$ is sufficienty differentiable scalar function then curl $$\left( {f\overrightarrow V } \right) = $$ _______.