Apr 22, 2015 · How do you prove that $$ \\Gamma'(1)=-\\gamma, $$ where $\\gamma$ is the Euler-Mascheroni constant?

Dec 17, 2023 · In principle, can a piecewise-defined function have a (nontrivial) piecewise-defined derivative, though? Sure, that's not an issue by any means, and sometimes is even an important …

7 You have to get the partial derivative with respect $\theta_j$. Remember that the hypothesis function here is equal to the sigmoid function which is a function of $\theta$; in other words, we need to apply …

Feb 17, 2020 · So when people say that the derivative is a slope, they either mean that it's a function that tells you the slope, or that a derivative evaluated at a certain point is a slope.

Apr 27, 2021 · And, when that happens, the derivative is indeed $\operatorname {sgn} (x)$ or $\frac x {|x|}$. But, since the derivative of the absolute value function is undefined at $0$, but $\operatorname …

Mar 9, 2023 · So, I was reading about the Dirac delta function and how its differentiation works. So, pretty much all texts and online sources I saw, define it using the integral: $$ \int_ {-\infty}^ {+\infty}x\df...

Jul 16, 2013 · 3 $\delta$ function is not strictly a function. If used as a normal function, it does not ensure you to get to consistent results. While mathematically rigorous $\delta$ function is usually not what …

Sep 4, 2015 · The derivative of a function of a discrete variable doesn't really make sense in the typical calculus setting. However, there is a continuous variant of the factorial function called the Gamma …

For others who end up here, this thread is about computing the derivative of the cross-entropy function, which is the cost function often used with a softmax layer (though the derivative of the cross-entropy …

Jun 21, 2017 · The absolute value function has a derivative (s) on restricted domains. i.e. f' (x) = -1 for x <0 and f' (x) = 1 for x > 0. However, the absolute value function is not "smooth" at x = 0 so the …