- #1
oliverkahn
- 27
- 2
In physics we often come across $$\rho=\dfrac{dq}{dV}$$ Does it mean:
##(i)## ##\displaystyle \lim_{\Delta V \to 0} \dfrac{\Delta q}{\Delta V}##
OR
##(ii)## ##\dfrac{\partial}{\partial z} \left( \dfrac{\partial}{\partial y} \left( \dfrac{\partial q}{\partial x} \right) \right)##
What does the first one mean?
The second one is a mixed partial derivative. Can it be found if ##q, \dfrac{\partial q}{\partial x}, \dfrac{\partial}{\partial y} \left( \dfrac{\partial q}{\partial x} \right)## are differentiable?
##(i)## ##\displaystyle \lim_{\Delta V \to 0} \dfrac{\Delta q}{\Delta V}##
OR
##(ii)## ##\dfrac{\partial}{\partial z} \left( \dfrac{\partial}{\partial y} \left( \dfrac{\partial q}{\partial x} \right) \right)##
What does the first one mean?
The second one is a mixed partial derivative. Can it be found if ##q, \dfrac{\partial q}{\partial x}, \dfrac{\partial}{\partial y} \left( \dfrac{\partial q}{\partial x} \right)## are differentiable?