Let's take the example of velocity of a particle in a flow field which depends on space(x,y,z) as well as on time(t).
V=f(x,y,z,t)
Partial derivative of velocity with respect to time=>∂V/∂t
Total derivative with respect to time=>dV/dt=∂V/∂t+(∂V/∂x)dx/dt+(∂V/∂y)dy/dt+(∂V/∂z)dz/dt
Now if say the flow is steady which quantity of the above two will be zero?Why the other one will not?
The total derivative of a function $f:\mathbb{R}^n \to \mathbb{R}$ at a given point $\textbf{x} \in \mathbb{R}^n$ is the unique linear transformation $\lambda:\mathbb{R}^n \to \mathbb{R}$ that best approximates the effect of $f$ near $\textbf{x}$, in the sense that
$\lim_{\textbf{h} \to \textbf{0}} \frac{\|f(\textbf{x+h}) - f(\textbf{x})-\lambda \textbf{h} \|}{\|\textbf{h}\|} = 0.$
Note that the linear transformation $\lambda$ very much depends on the point $\textbf{x}$ in question, and is usually denoted by $Df(\textbf{x})$.
So total differentiation is a process by which we can locally approximate a non-linear function by a linear function.
Continuing on, the $i$th partial derivative of $f$ at $\textbf{x}$ is the real number
$\frac{\partial f}{\partial x^i}(\textbf{x}) = \lim_{t \to 0} \frac{f(\textbf{x}+t\textbf{e}_i)-f(\textbf{x})}{t}.$
So partial derivatives also convey the effect of $f$ near $\textbf{x}$, but only as one approaches $\textbf{x}$ from a specific direction. And as $\textbf{x}$ is allowed to vary, $\partial f / \partial x^i$ becomes a function $\mathbb{R}^n \to \mathbb{R}$, but this partial derivative function can be far from linear.
I can't speak much about physics, but there are plenty of functions $\mathbb{R}^n \to \mathbb{R}$ which are differentiable at a specific point $\textbf{x} \in \mathbb{R}^n$, with a total derivative at $\textbf{x}$ that is nonconstant, but still having some partial derivative functions that are constant on all of $\mathbb{R}^n$
An example of this would be $f:\mathbb{R}^3 \to \mathbb{R}\, ;\, (x,y,z) \mapsto x^2 + y+z$.