Comments on: Automatic Differentiation http://artent.net/2012/08/19/automatic-differentiation/ We're blogging machines! Wed, 15 Jan 2025 16:08:06 +0000 hourly 1 http://wordpress.org/?v=4.0 By: hundalhh http://artent.net/2012/08/19/automatic-differentiation/#comment-2998 Mon, 17 Mar 2014 05:34:03 +0000 http://162.243.213.31/?p=480#comment-2998 The derivative of x^x with respect to x is x^x *(log(x) + 1).
The derivative of x^k with respect to x is k*x^(k-1).
The derivative of k^x with respect to x is k^x *log(k).

If f(x) and g(x) are a functions of x, with derivatives f'(x) and g'(x)
The derivative of f(x)^g(x) with respect to x is

f(x)^g(x)( g(x)*f'(x)/f(x) + log(f(x))*g'(x))

The derivative of f(x)^k is k*f(x)^(k-1)*f'(x).
The derivative of k^(f(x)) is k^f(x) *log(k)*f'(x).

You might want to check out wolframalpha.com.

]]> By: Young http://artent.net/2012/08/19/automatic-differentiation/#comment-2878 Tue, 25 Feb 2014 08:55:32 +0000 http://162.243.213.31/?p=480#comment-2878 Hi, I also discovered automatic differentiation today, and it was really interesting. I studied about it for a while. But I couldn’t find out how I can hadle the function,’y=x^x’. Could you tell me about it or inform me any sites that handles the function?

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