Also known as a **variational derivative**, the functional derivative of a functional $$J[f]$$ is denoted $$\frac{\partial}{\partial f(\mathbf{x})} J$$, and is defined as the derivative of $$J$$ with respect to the value of the function $$f$$ at the point $$\mathbf{x}$$.

Functional Derivative

A function of a function $$f$$ is called a **functional** $$J[f]$$.

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The **calculus of variations** is a mathematical tool used to solve optimization problems where the goal is to find an optimal function rather than a set of parameters. For example, it can be used to choose a function that minimizes a given cost functional.

Calculus of variations

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

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