- Problem Statement
- Trying to calculate ##\frac{d}{dt}dx##

- Relevant Equations
- Trying to calculate ##\frac{d}{dt}dx##

here I am trying to find ##\frac{d}{dt}dx## where ##x(t)## is the position vector

Now ##\frac{d}{dt}(v_x(x,y,z,t)dt)=\frac{dv_x}{dt}dt=\frac{\partial v_x}{\partial t}dt+\frac{\partial v_x}{\partial x}dx+\frac{\partial v_x}{\partial y}dy+\frac{\partial v_x}{\partial z}dz##

Now dividing by ##dx##

##\frac{\partial v_x}{\partial t}\frac{dt}{dx}+\frac{\partial v_x}{\partial x}##

Other terms goes to zero.

It therefore becomes ##\frac{\partial v_x}{\partial t}\frac{\partial t}{\partial x}+\frac{\partial v_x}{\partial x}=\frac{\partial v_x}{\partial x}+\frac{\partial v_x}{\partial x}=2\frac{\partial v_x}{\partial x}##

Am I right in doing so??

Now ##\frac{d}{dt}(v_x(x,y,z,t)dt)=\frac{dv_x}{dt}dt=\frac{\partial v_x}{\partial t}dt+\frac{\partial v_x}{\partial x}dx+\frac{\partial v_x}{\partial y}dy+\frac{\partial v_x}{\partial z}dz##

Now dividing by ##dx##

##\frac{\partial v_x}{\partial t}\frac{dt}{dx}+\frac{\partial v_x}{\partial x}##

Other terms goes to zero.

It therefore becomes ##\frac{\partial v_x}{\partial t}\frac{\partial t}{\partial x}+\frac{\partial v_x}{\partial x}=\frac{\partial v_x}{\partial x}+\frac{\partial v_x}{\partial x}=2\frac{\partial v_x}{\partial x}##

Am I right in doing so??