The Student Room Group

Change of Variables/Partial Derivatives

hi

struggling to get my head round some partial derivatives/change of variables

if z = z(x,y) and then x = x (v,t) then what is the partial derivative of z with respect to v?

my current thinking atm is writing it out like: [d ( x (v,t), y)]/dv

but don't really know how to carry it out? any help?
Use the chain rule.

If it is only x that depends on v, then dz/dv = dz/dx dx/dv.

However if y also depends on v, then dz/dv = dz/dx dx/dv + dz/dy dy/dv.

Quick Reply