Please help me on the following derivative:
How to take derivative of \int f(x)lnf(x)dx on f(x)?
Thanks in advance.
n*******l 发帖数: 2911
2
Let J(f) = \int f(x) lnf(x) dx. Define
j(t) := J(f+tg) = \int (f+tg) ln(f+tg).
j'(t) = \int gln(f+tg) + g.
j'(0) = \int (lnf+1)g.
The functioanl derivative of J with respect to f is then
lnf+1.
【在 z*******e 的大作中提到】 : Please help me on the following derivative: : How to take derivative of \int f(x)lnf(x)dx on f(x)? : Thanks in advance.
z*******e 发帖数: 24
3
Thanks!
【在 n*******l 的大作中提到】 : Let J(f) = \int f(x) lnf(x) dx. Define : j(t) := J(f+tg) = \int (f+tg) ln(f+tg). : j'(t) = \int gln(f+tg) + g. : j'(0) = \int (lnf+1)g. : The functioanl derivative of J with respect to f is then : lnf+1.
