Partial Derivatives: f(x,y)=e^(3x+9y) Find fsubxx

In summary, a partial derivative is a mathematical concept denoted by the symbol ∂ that measures the rate of change of a function with respect to one of its variables while holding all other variables constant. Its purpose is to understand how a function changes in response to changes in its variables and it can be used to optimize functions in various fields. To find a partial derivative, all other variables are treated as constants and the function is differentiated with respect to the variable of interest. Fsubxx represents the second partial derivative of the function with respect to x, measuring the rate of change of the function's slope with respect to x.
  • #1
MathNoob123
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0

Homework Statement


f(x,y)=e^(3x+9y)
find fsubxx


Homework Equations





The Attempt at a Solution


I got e^(3x+9y)3, but the stupid web assign won't take it as an answer. I am pretty sure this is the correct answer. Am i wrong? Please help =).
 
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  • #2
First, I would reorder the way you write the answer to avoid confusion.

Second (hint), what is the difference in fx and fxx
 

1. What is a partial derivative?

A partial derivative is a mathematical concept that measures the rate of change of a function with respect to one of its variables while holding all other variables constant.

2. How is a partial derivative denoted?

A partial derivative is denoted by the symbol ∂, pronounced "del," and the variable with respect to which the derivative is taken is written to the right of the symbol. For example, ∂f/∂x represents the partial derivative of f with respect to x.

3. What is the purpose of finding a partial derivative?

The purpose of finding a partial derivative is to understand how a function changes in response to changes in its variables. It can also be used to optimize functions in fields such as economics, engineering, and physics.

4. How do you find a partial derivative?

To find a partial derivative, you treat all other variables as constants and differentiate the function with respect to the variable of interest. For example, in the function f(x,y)=e^(3x+9y), the partial derivative with respect to x would be 3e^(3x+9y) and the partial derivative with respect to y would be 9e^(3x+9y).

5. What is the meaning of fsubxx in the given function?

fsubxx represents the second partial derivative of the function f with respect to x. This means that we are taking the partial derivative of the function's first partial derivative with respect to x. In other words, it measures the rate of change of the function's slope with respect to x.

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