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ohlala191785
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Homework Statement
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
Homework 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)).
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!