# How to differentiate e^(x+y) for x?

• gtfitzpatrick
In summary, dy/dx cannot be determined without more information, but implicit differentiation can be used to find its value in certain cases.
gtfitzpatrick

## Homework Statement

if f(x,y) is e^(x+y) am i right in saying dy/dx is e^(x+y)

## The Attempt at a Solution

If y is not a function of x, dy/dx makes no sense at all! (Except for dy/dx= 0.)
The notation f(x,y)= ex+y implies that x and y are independent variables. Without further information, you can find $\partial f/\partial x$ or $\partial f/\partial y$ but not dy/dx.

If, for example, you know that f(x,y)= ex+y= constant, then you can use "implicit differentiation": (1+ dy/dx)ex+y= 0 and determine that dy/dx= -1.

## 1. What is the general formula for differentiating e^(x+y) for x?

The general formula for differentiating e^(x+y) for x is e^(x+y).

## 2. How do you differentiate e^(x+y) for x?

To differentiate e^(x+y) for x, we use the chain rule. First, we take the derivative of the exponent (x+y) which is 1. Then, we multiply it by the derivative of the base (e^(x+y)) which is e^(x+y). Therefore, the final answer is e^(x+y).

## 3. Can I use the product rule to differentiate e^(x+y) for x?

No, you cannot use the product rule to differentiate e^(x+y) for x. The product rule is used for differentiating two functions that are multiplied together, but in this case, e^(x+y) is a single function.

## 4. Is the differentiation of e^(x+y) for x the same as the differentiation of e^x for x?

No, the differentiation of e^(x+y) for x and e^x for x are not the same. The former involves differentiating a function with two variables (x and y) while the latter involves differentiating a function with only one variable (x).

## 5. Are there any special cases to consider when differentiating e^(x+y) for x?

No, there are no special cases to consider when differentiating e^(x+y) for x. The general formula (e^(x+y)) applies to all cases and there are no exceptions.

• Calculus and Beyond Homework Help
Replies
8
Views
825
• Calculus and Beyond Homework Help
Replies
18
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
718
• Calculus and Beyond Homework Help
Replies
7
Views
761
• Calculus and Beyond Homework Help
Replies
14
Views
501
• Calculus and Beyond Homework Help
Replies
25
Views
595
• Calculus and Beyond Homework Help
Replies
10
Views
575
• Calculus and Beyond Homework Help
Replies
2
Views
827
• Calculus and Beyond Homework Help
Replies
2
Views
363
• Calculus and Beyond Homework Help
Replies
2
Views
362