Partial Derivative

# Partial Derivative

## What is Partial Derivative

A partial derivative is a derivative taken with respect to one of a function’s variables, while the other variables are held constant. Partial derivatives are used in physics, engineering, and mathematics to solve problems involving functions of several variables.

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## What is The Definition of Partial Differentiation?

The definition of partial differentiation is the process of differentiating a function with respect to one of its variables, while keeping the other variables constant.

## What is the Symbolic Representation of Partial Differentiation?

In mathematics, partial differentiation is the operation of finding the derivative of a function with respect to one of its variables, while keeping the other variables constant. The symbol for partial differentiation is ∂, the derivative symbol with a bar over it.

## What is the Definition for Partial Derivative

A partial derivative is a derivative taken with respect to one or more variables, while other variables are held constant. Partial derivatives are important in calculus and mathematical physics.

## What are the rules for Partial Derivative?

The rules for partial derivatives are as follows:

1. The derivative of a function with respect to a single variable is the derivative of the function with respect to that variable, multiplied by the derivative of the variable with respect to the other variable.

2. The derivative of a function with respect to a vector is the derivative of the function with respect to each variable, multiplied by the derivative of the vector with respect to that variable

## What is Product Rule for the Partial Derivative

The product rule for the partial derivative is a mathematical formula that helps to calculate the derivative of a product of two functions. The product rule for the partial derivative is written as:

d/dx (f(x) * g(x)) = f'(x) * g(x) + f(x) * g'(x)

## What is Quotient Rule for the partial derivative?

The partial derivative of a function ƒ at a point x is the derivative of ƒ with respect to x, holding all other variables constant. The quotient rule for the partial derivative states that the derivative of the function ƒ at x divided by the derivative of x with respect to x is equal to the derivative of ƒ with respect to y multiplied by y’:

ƒ'(x) ÷ ƒ'(x) = ƒ'(y) × y'(x)

## What is Power Rule for the partial derivative?

The power rule for the partial derivative is a mathematical rule that helps to calculate the derivative of a function that is composed of a product of two or more functions. The power rule states that the derivative of a function composed of a product of two or more functions is the derivative of the first function multiplied by the derivative of the second function.

## What is Partial Derivative Chain Rule

The partial derivative chain rule states that the derivative of a function of a function is equal to the derivative of the function of the first function, multiplied by the derivative of the function of the second function.

## What is the Chain Rule for The Independent Variable

The Chain Rule for the independent variable states that the derivative of the dependent variable with respect to the independent variable is equal to the derivative of the dependent variable with respect to the independent variable multiplied by the derivative of the independent variable with respect to the independent variable.

## What is Chain Rule for The Dependent Variable

The Chain Rule is a mathematical formula that helps calculate the derivative of a function that is composed of two or more functions. In the context of calculus, the Chain Rule is used to find the derivative of a composite function
f(x) = g(h(x)).

## What is The Partial Derivative of Natural Logarithm (In)

The partial derivative of the natural logarithm is the derivative of the natural logarithm function with respect to one of its variables.

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