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

Functional Derivatives

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

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The calculus of variations is a mathematical tool that helps with solving an optimization problem with respect to a function. 

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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