# Derivative of a multi-variable function

• raining
In summary, the question is asking to differentiate the expression (2nb^{rx}+n)^{k} without specifying which variable the derivative should be taken with respect to. It is possible that there is only one variable, x, in this expression and all other letters represent constants. However, in a more complex expression such as ysin(x)+e^{x^{2}y}=\sqrt{x+y}, both x and y could be variables. In this case, it may be necessary to use partial derivatives or implicit differentiation to find the derivative.
raining
The question asks to differentiate (2nb$^{rx}$+n)$^{k}$

However, the problem is that it doesn't specify with respect to which variable should the derivative be taken.

When the question asks to differentiate, does it mean that we should take the derivative for each and every variable, one by one?

raining said:
The question asks to differentiate (2nb$^{rx}$+n)$^{k}$

However, the problem is that it doesn't specify with respect to which variable should the derivative be taken.

When the question asks to differentiate, does it mean that we should take the derivative for each and every variable, one by one?
I'm guessing that there is only one variable here - x - and all other letters represent constants.

Ok, then what about in a question such as ysin(x)+e$^{x^{2}y}$=$\sqrt{x+y}$

This is what is confusing me.

In this case will both x and y be variables?

Last edited:
In that case I would suggest the partial derivatives.

Although, strictly speaking, the fact that the partial derivatives exist at a point does not prove that the fuction is "differentiable"- but the fact that they are continuous does. To be perfectly correct, the "derivative" of a two variable function is the linear transformation from R2 to R given by taking the dot product of $\nabla f\cdot <x, y>$ and so can be represented by $\nabla f$.

raining said:
Ok, then what about in a question such as ysin(x)+e$^{x^{2}y}$=$\sqrt{x+y}$

This is what is confusing me.

In this case will both x and y be variables?

Perhaps it is an implicit differentiation exercise with y understood to be a function of x defined implicitly. Then you would calculate ##\frac{dy}{dx}## implicitly.

## What is a multi-variable function?

A multi-variable function is a mathematical function that has more than one independent variable. This means that the output of the function is dependent on multiple input variables.

## What is the derivative of a multi-variable function?

The derivative of a multi-variable function is a mathematical concept that represents the rate of change of the function with respect to its input variables. It measures how much the output of the function changes when the input variables are changed.

## How is the derivative of a multi-variable function calculated?

The derivative of a multi-variable function is calculated using partial derivatives. This involves taking the derivative of the function with respect to each input variable, while holding the other variables constant.

## Why is the derivative of a multi-variable function important?

The derivative of a multi-variable function is important because it allows us to understand how the function changes in response to changes in its input variables. This information is useful in fields such as physics, engineering, and economics.

## What are some real-world applications of the derivative of a multi-variable function?

The derivative of a multi-variable function has many real-world applications, such as optimizing production processes in manufacturing, predicting stock market trends, and designing efficient transportation routes. It is also used in machine learning and data analysis to understand relationships between multiple variables.

Replies
1
Views
854
Replies
8
Views
1K
Replies
9
Views
1K
Replies
4
Views
2K
Replies
5
Views
2K
Replies
5
Views
770
Replies
7
Views
846
Replies
9
Views
1K
Replies
13
Views
1K
Replies
10
Views
1K