# Derivative with dotproduct

by Nickel   Last Updated May 15, 2019 16:20 PM

Given a function $$f: \mathbb{R^{n}} \to \mathbb{R}$$, $$A \in \mathbb{R}^{n\times n}, x,b \in \mathbb{R}^n$$. What is the derivative of $$f(x) = \langle x, Ax \rangle + \langle b, x \rangle + c$$, at the point $$x_0$$?

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The gradient of $$f$$ at $$x_0$$ is $$\nabla f(x)_0 = (A+A^\top)x_0 + b$$. For reference, you can consult the matrix cookbook, for example, or any other relevant textbook.

Pantelis Sopasakis
May 15, 2019 16:03 PM

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