## Fréchet derivative of the (matrix) exponential function

$$ D\exp(x)u = \int_0^1 e^{sx}ue^{(1-s)x}\,ds. $$ This intriguing formula expresses the derivative of the exponential map on a Banach algebra as an integral. In...

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# Month: February 2013

## Fréchet derivative of the (matrix) exponential function

## Convex functions, second derivatives and Hessian matrices

## Differentiation done correctly: 5. Maxima and minima

## Differentiation done correctly: 4. Inverse and implicit functions

## Differentiation done correctly: 3. Partial derivatives

## Differentiation done correctly: 2. Higher derivatives

## Differentiation done correctly: 1. The derivative

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$$ D\exp(x)u = \int_0^1 e^{sx}ue^{(1-s)x}\,ds. $$ This intriguing formula expresses the derivative of the exponential map on a Banach algebra as an integral. In...

In single variable calculus, a twice differentiable function \(f:(a,b)\to\mathbb{R}\) is convex if and only if \(f^{\prime\prime}(x)\ge 0\) for all \(x\in(a,b)\...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima In this final post, we...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima Now we’re going ...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima While we saw that diff...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima Last time, we covered ...

Navigation: 1. The derivative | 2. Higher derivatives | 3. Partial derivatives | 4. Inverse and implicit functions | 5. Maxima and minima In multivariable calcu...