1. The problem statement, all variables and given/known data Show that the operation of taking the gradient of a function has the given property. Assume u and v are differentiable functions of x and y and that a and b are constants. Operation: (∇(u))n = n*un-1*∇u 2. Relevant equations The gradient vector of f is <∂f/∂x,∂f/∂y>, where f is a function of x and y (in other words f(x,y)). 3. The attempt at a solution I tried proof by induction, but I have a lot of gaps. Base, n=1: ∇u = n*u0∇u. But what is u0 if u is a function? Assume n = k: ∇uk = n*uk-1∇u For k=k+1, ∇uk+1 = n*uk∇u. Isn't proof by induction for sums though? I can't seem to identify the sum here. Any help would be greatly appreciated!