How do you do implicit differentiation of three variables as in V=XYZ. I just need to know how to differentiate XYZ.

Question

anonymous · Answer

Is x y z all variable?

anonymous · Answer

yes

anonymous · Answer

I just need to differentiate V=LWH. Do I need to find a value for one first? using implicit differentiation.

anonymous · Answer

If X and Y and Z  are all variable, you need to use partial differentiation

$$dv/dx=yz$$
$$dv/dy=xz$$
$$dv/dz=yx$$
incorrect symbol for partial

anonymous · Answer

I don't think we learned that. Its a related rates problem if that makes a difference

anonymous · Answer

That's the differential
$$dv=yz  dx+xz  dy  +xy  dz$$

anonymous · Answer

I have to find a relationship between two of the variables to eliminate one I think. Thanks for your help. I figured it out!

anonymous · Answer

take the gradient of the function XYZ and dot it with (dx,dy,dz)

anonymous · Answer

Since it is related rate, maybe this
$$dv/dt=yz   dx/dt+xz dy/dt+ xy  dz/dt$$