※ 引述《cotton757 (cotton757)》之銘言：
: __
: For each of the following functions, find the derivative vector \/f(x) for
: n
: those points x in R where is defined :
: 2
: ||x|| n
: 1.f(x) = e for x in R
Let x=(x1,x2,...,xn).Then f(x)=exp[(x1)^2+(x2)^2+...+(xn)^2].
pf(x)/p(xi)=2(xi)exp[(x1)^2+(x2)^2+...+(xn)^2]=2(xi)f(x),i=1,2,...,n.
[ps. p:partial derivative.]
So,▽f(x)=2f(x)·(x1,x2,...,xn).
: 1 3
: 2.f(x) = --------- for x in A = {x in R |x =/= 0}
: ||x||^2
Let x=(x1,x2,...,xn).Then f(x)=[(x1)^2+(x2)^2+...+(xn)^2]^(-1).
pf(x)/p(xi)=-[(x1)^2+(x2)^2+...+(xn)^2]^(-2)·2xi=-2xi[f(x)]^2.
So,▽f(x)=-2{[f(x)]^2}(x1,x2,...,xn).
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