
Re: Derivative of a multivariable function by another multivariable function
Posted:
Apr 6, 2013 3:12 AM


On Fri, 5 Apr 2013, henuaenata wrote: > > I am trying to figure out how to write the derivative of a multivariable > function by another multivariable function. > > For example, how to derive f(x,y,z) with respect to g(x,y): âHBf(x,y,z)/âHBg(x,y)
First off, don't use fancy confusing characters, use plain text only. Secondaly, I doubt there is such a thing. However, symbolically
df(x,y,z)/dt = f_x(x,y,z).dx/dt + f_y(x,y,z).dy/dt + f_z(x,y,z).dz/dt
Let t = g(x,y); dz/dt = 0; dt/dx = g_x(x,y); dt/dy = g_y(x,y), df(x,y,z)/dg(x,y) = f_x(x,y,z)/g_x(x,y) + f_y(x,y,z)/g_y(x,y).

