Find fyy (x,y): Partial Derivative of x2y3 + x4y + xe2y

In summary, a partial derivative is a mathematical concept used to determine the rate of change of a function with respect to one of its variables, while holding all other variables constant. It differs from regular derivatives in that it only focuses on one variable at a time. To find partial derivatives, the variable of interest is identified and treated as the only variable in the function, while all others are treated as constants. The partial derivative of a given function can be found by using the power rule for each variable in the function. For the specific function x<sup>2</sup>y<sup>3</sup> + x<sup>4</sup>y + xe<sup>2y</sup>, the partial derivative with respect to x is
  • #1
hthorne21
3
0
Find fyy (x,y) where f(x,y) = x2y3 + x4y + xe2y
 
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  • #2
This is the part where you show your attempt. Also use ^ to denote power, I assume x2y3 means x^2 y^3. If you know TeX you can write that as [tex]x^2y^3[/tex]
 
  • #3
Try this: replace every x with the constant a... now the equation should look like it is in one variable, y. So what you need now is to find the second derivative with respect to y. Does that make life easier?
 

Related to Find fyy (x,y): Partial Derivative of x2y3 + x4y + xe2y

1. What is a partial derivative?

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

2. What is the difference between partial derivatives and regular derivatives?

Partial derivatives are used to determine the rate of change of a function with respect to one variable, while keeping all other variables constant. Regular derivatives, on the other hand, determine the rate of change of a function with respect to a single variable.

3. How do you find partial derivatives?

To find partial derivatives, you must first identify the variable that you are differentiating with respect to. Then, treat all other variables as constants and use the power rule to differentiate the function. Repeat this process for each variable in the function.

4. What is the partial derivative of x2y3 + x4y + xe2y with respect to x?

The partial derivative of x2y3 + x4y + xe2y with respect to x is 2xy3 + 4x3y + e2y.

5. What is the partial derivative of x2y3 + x4y + xe2y with respect to y?

The partial derivative of x2y3 + x4y + xe2y with respect to y is 3x2y2 + x4 + 2xe2y.

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