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

[Teachme]

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

 

[SammyS]

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 2^y is also a constant.

 

[Bacle2]

Have you considered using the identity:

a^b =e^{bloga} ?

 

[HallsofIvy]

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]