# Scalar Derivative and Partial Derivatives

## Derivative

In calculus, **derivative **can be approached in two different ways. One is geometrical (as a **slope of a curve**) and the other one is physical (as a **rate of change**).** **The process of finding a **derivative **is called "**differentiation**"

**'The derivative of'** is commonly written as $\frac{d}{dx}$ or $f'(x)$

### Find a Derivative

#### Example:

$f'(x)=\frac{d}{dx}x^2 = 2x$

means the slope or "rate of change" at any point in the graph/function $x^2$ is **2x**. So when **x=2** the slope is **2x = 4**

### Scalar derivative rules

## Partial Derivatives

A **partial derivative** of a function of several variables is its derivative with respect to one of those variables, with the others held constant.

**'The partial derivative with respect to x'** is written as $\frac{\partial f}{\partial x}$ or $f'_x$where ${\partial}$is called 'del' or 'curly dee'.

### Find Partial Derivatives

Consider a function with two variables (x and y): $f(x,y) = x^2 + y^3$

**a) Partial derivative with respect to x **(Treat y as a constant like a random number 12)

**b) Partial derivative with respect to y **(Treat x as a constant)

Link: - Matrix Calculus For Deep Learning - MathIsFun: Introduction to Derivatives - MathIsFun: Partial Derivatives - Khan Academy: Basic Derivative Rules

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