- #1
Apashanka
- 429
- 15
- Homework 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??