Partial derivative of fx(x,y)= x^7 + 2^y + x^y with respect to x

In summary, the person is trying to find information on how to solve an equation for y, but is not seeing anything with respect to x. They are using the partial derivative and know how to do it for y, but are not seeing anything with respect to x. They think that the answer is 7x^6+yx^(y-1), but according to cramster this does not have a 1 in it. They think that y itself is 0, but it is not.
  • #1
Teachme
72
0

Homework Statement


I can't seem to find information on this specific question i have.

So I'm taking the partial derivative of this equation for both x and y
I know how to do it for y, but I am not seeing something with respect to x
fx(x,y)= x^7 + 2^y + x^y

Homework Equations


The Attempt at a Solution



So this is what I thought it should be 7x^6 + 1 + yx^(y-1)I guess the answer is 7x^6+yx^(y-1) according to cramster and there is no 1 in it.Why does 2^y not go to 1?

I would think because you treat y as a constant that it would go to zero and 2^0 is 1
What is wrong with my reasoning? Thanks for reading
 
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  • #2
Teachme said:

Homework Statement


I can't seem to find information on this specific question i have.

So I'm taking the partial derivative of this equation for both x and y
I know how to do it for y, but I am not seeing something with respect to x
fx(x,y)= x^7 + 2^y + x^y

Homework Equations



The Attempt at a Solution



So this is what I thought it should be

7x^6 + 1 + yx^(y-1)

I guess the answer is 7x^6+yx^(y-1) according to cramster and there is no 1 in it.

Why does 2^y not go to 1?

I would think because you treat y as a constant that it would go to zero and 2^0 is 1
What is wrong with my reasoning?

Thanks for reading

If you treat y as a constant, then 2y is also a constant.
 
  • #3
Have you considered using the identity:

a^b =e^{bloga} ?
 
  • #4
Teachme said:

Homework Statement


I can't seem to find information on this specific question i have.

So I'm taking the partial derivative of this equation for both x and y
I know how to do it for y, but I am not seeing something with respect to x
fx(x,y)= x^7 + 2^y + x^y

Homework Equations





The Attempt at a Solution



So this is what I thought it should be


7x^6 + 1 + yx^(y-1)


I guess the answer is 7x^6+yx^(y-1) according to cramster and there is no 1 in it.


Why does 2^y not go to 1?

I would think because you treat y as a constant that it would go to zero and 2^0 is 1
What is wrong with my reasoning?
First, stop even thinking Z"it goes to"! That is too vague and you are confusing yourself. The derivative of a constant is 0 but that does NOT mean that y itself is 0.


[/quote]Thanks for reading[/QUOTE]
 

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, holding all other variables constant. It is written using the symbol ∂ and can be thought of as a slope of a tangent line on a multi-dimensional graph.

2. How is a partial derivative different from a regular derivative?

A regular derivative measures the rate of change of a function with respect to a single variable, while a partial derivative measures the rate of change with respect to one variable while holding all others constant. In other words, a partial derivative is like taking a regular derivative with blinders on, only considering the effect of one variable on the function.

3. What is the purpose of finding partial derivatives?

Partial derivatives are used in many fields of science and engineering, including physics, economics, and statistics. They are helpful in understanding how a function changes in relation to its variables, and can be used to optimize functions, make predictions, and solve complex problems.

4. How do you calculate a partial derivative?

To calculate a partial derivative, you take the derivative of the function with respect to the variable you are interested in while treating all other variables as constants. This can be done using the standard rules of differentiation, such as the power rule and chain rule.

5. Can a function have multiple partial derivatives?

Yes, a function can have multiple partial derivatives, as there can be multiple variables in a function. Each partial derivative represents the rate of change of the function with respect to one variable, while holding all others constant. So, a function with two variables would have two partial derivatives, and a function with three variables would have three partial derivatives.

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