Partial Derivatives

Partial differentiation is the same as regular differentiation, but it keeps all variables in a multivariable function the same except for one variable.  The partial derivative d/dx(f(a,b,c,...x,y,z)) can be defined through the limit definition: d/dx(f(a,b,c,...x,y,z)) = lim(h->0) (f(a,b,c...,x + h,y,z) - f(a,b,c,...,x,y,z))/h.  For example, the derivative of f(x, y)=xy is lim(h->0) (f(x + h,y) - f(x,y))/h) = lim(h->0) (((x + h)y - xy)/h) = lim(h->0) ((xy + hy - xy)/h) = lim(h->0) (hy/h) = y.