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Homework Statement
Let f:Rnxn-->Rnxn be defined by f(A) = A2. Prove that f is differentiable. Find the derivative of f.
Homework Equations
f(a + h) = f(a) + f'(a)h + [itex]\phi[/itex](h)
The Attempt at a Solution
f(A + H) = (A + H)2 = A2 + AH + HA + H2
f(A) is given by A2. So the sum of the derivative operator and the remainder term is AH + HA + H2. The problem is that I don't know how to determine which terms are part of the derivative.