My Math Forum Differentiating the gradient?

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 January 20th, 2009, 01:46 AM #1 Newbie   Joined: Jan 2009 Posts: 2 Thanks: 0 Differentiating the gradient? Hi! This problem arises when trying to do a Newton-step in an optimization problem: Stating from t0=0 i wish to take the step t1 = -dP'(0)/dt / d²P''(0)/dt² , where P=f(x+td) and f is a given function. Thus, dP(x)/dt must equal grad(f(x+td))'*d, which for t=0 -> P'(0)=grad(f(x))'*d. Everytinh fine so far. But how to derive d²P''(0)/dt²?? It's essentially a question about differentiating the gradient, something I am not sure as to how to go about. Thanks in advance
 January 20th, 2009, 02:20 AM #2 Newbie   Joined: Jan 2009 Posts: 2 Thanks: 0 Re: Differentiating the gradient? On a second thought, though, couldn't this be written as the derivative component-wise? I.e. with my P(t) as: d²P''(0)/dt²=laplacian(f(x+td))'*d²

### dÂ²p/dtÂ²=0

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