# Category:Examples of Partial Derivatives

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This category contains examples of **partial derivatives**.

The **partial derivative of $f$ with respect to $x_i$ at $a$** is denoted and defined as:

- $\map {\dfrac {\partial f} {\partial x_i} } a := \map {g_i'} {a_i}$

where:

- $g_i$ is the real function defined as $\map g {x_i} = \map f {a_1, \ldots, x_i, \dots, a_n}$
- $\map {g_i'} {a_i}$ is the derivative of $g$ at $a_i$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Examples of Partial Derivatives"

The following 33 pages are in this category, out of 33 total.

### P

- Partial Derivative of Hamiltonian with respect to Displacement
- Partial Derivative of Hamiltonian with respect to Momentum
- Partial Derivative of Hamiltonian with respect to Time
- Partial Derivative wrt x of sin x y over cos (x + y)
- Partial Derivative wrt z of z^2 equals x^2 - 2 x y - 1 at (1, -2, -2)
- Partial Derivative wrt z of z^2 equals x^2 - 2 x y - 1 at (1, -2, -2)/Implicit Method
- Partial Derivative/Examples
- Partial Derivative/Examples/2 u + 3 v = sin x, u + 2 v = x cos y
- Partial Derivative/Examples/Arbitrary Cubic
- Partial Derivative/Examples/Notation for 3-Value Function
- Partial Derivative/Examples/u + ln u = x y
- Partial Derivative/Examples/u - v + 2 w, 2 u + v + 2 w, u - v + w
- Partial Derivative/Examples/u^2 + v^2 = x^2, 2 u v = 2 x y + y^2
- Partial Derivative/Examples/u^2 + x^2 + y^2 = a^2
- Partial Derivative/Examples/v + ln u = x y, u + ln v = x - y
- Partial Derivative/Examples/v + ln u = x y, u + ln v = x - y/Second Partial Derivative
- Partial Derivative/Examples/x sine y z
- Partial Derivative/Examples/x z^y
- Partial Derivative/Examples/x^(x y)
- Partial Derivative/Examples/x^(x y)/wrt x
- Partial Derivative/Examples/x^(x y)/wrt y
- Partial Derivatives of tan^2 (x^2 - y^2)
- Partial Derivatives of u^2 + x^2 + y^2, u - v^3 + 3 x
- Partial Derivatives of x ln y^2 + y e^z
- Partial Derivatives of x tan^-1 (x^2 + y)
- Partial Derivatives of x^u + u^y
- Partial Derivatives of x^y^z