How to Find y^m When y = x^(-3) + x

[priscilla98]

Homework Statement

y = x^ -3 + x. Find y^m.

The Attempt at a Solution

I'm a little confused on how to find y^m. Would I use the derivatives to find this?

For example:

y = x^ -3 + x

y = -2x^ -2 + x

Okay now I am confused by this

 

[Mark44]

Homework Statement

y = x^ -3 + x. Find y^m.

The Attempt at a Solution

I'm a little confused on how to find y^m. Would I use the derivatives to find this?

For example:

y = x^ -3 + x

y = -2x^ -2 + x

Okay now I am confused by this

I don't see that this problem has anything to do with derivatives. y^m ordinarily indicates that y is being raised to a power, so that y² would be (x^-3 + x)².

If the problem asks for y^(m), with parentheses around the exponent, then that typically indicates the mth derivative.

Your examples don't make any sense. If y = x^-3 + x, then y won't also be equal to -2x^{-2UP] + x.}

 

[priscilla98]

I don't see that this problem has anything to do with derivatives. y^m ordinarily indicates that y is being raised to a power, so that y² would be (x^-3 + x)².

If the problem asks for y^(m), with parentheses around the exponent, then that typically indicates the mth derivative.

Your examples don't make any sense. If y = x^-3 + x, then y won't also be equal to -2x^{-2UP] + x.}

^{Okay since y^m = y^2 and you state because of this y = (-x^3 + x)^2. Now, would you evaluate this equation further?}

 

[priscilla98]

y = -x^3 + x is also similar to the graph of y = x^3 except that this graph is the opposite of y = x^3

 

[priscilla98]

Okay this is a multiple choice question

a) -6
b) -60x^-6
c) -60x^-6 + x^-2
d) -60x^-6 - x^-2

When I put y = -x^3 + x on my graphing calculator. I see the coordinates (-4, 60) and (4, -60)

 

[Mark44]

What exactly is the question? Are you given m? I don't see any connection between the answers you show and the problem as you have stated it.

 

[priscilla98]

What exactly is the question? Are you given m? I don't see any connection between the answers you show and the problem as you have stated it.

Okay, then this is the whole question::: But this is a multiple choice question

y = x^ -3 + x. Find y^m.

a) -6
b) -60x^-6
c) -60x^-6 + x^-2
d) -60x^-6 - x^-2

 

[priscilla98]

I really do appreciate the help, thanks. It's just that I'm really confused on this equation.

 

[dirk_mec1]

The question is probably:

y = x^ {-3} + x.

Find y"'.

a) -6
b) -60x^-6
c) -60x^-6 + x^-2
d) -60x^-6 - x^-2

 

[priscilla98]

That would probably be it. So, now it be would be y = (x^-3 + x)^3, right?

 

[Mark44]

That would probably be it. So, now it be would be y = (x^-3 + x)^3, right?

Well, is it or isn't it? Where are you getting the m? Here we are at post #11 in this thread, and we don't even know what the problem is yet.

It's impossible for us to help you if you don't even know what the problem is asking for. Are you misreading ''' as m? The ''' notation indicates the third derivative, and m indicates the mth power of what it is an exponent on.

 

[priscilla98]

Well, is it or isn't it? Where are you getting the m? Here we are at post #11 in this thread, and we don't even know what the problem is yet.

It's impossible for us to help you if you don't even know what the problem is asking for. Are you misreading ''' as m? The ''' notation indicates the third derivative, and m indicates the mth power of what it is an exponent on.

I'm getting the m from the problem. It states as my first post is

y = x^-3 + x. Now, find y^m. I have even given the multiple choices for this question. You're right, you can' really help me if I don't understand it. Okay, now you state that first the mth derivative was the second now it's a third, fine okay. But by using the mth derivative would we use dx/dy? I know I am confused on this that's why I posted this question. But i don't understand how this question leads to the choices below

a) - 6
b) -60x^-6
c) -60x^-6 + x^-2
d) -60x^-6 - x^-2

 

[Mark44]

y^m doesn't lead to any of the choices given, but y^(m) does for one value of m. The notation of an exponent in parentheses usually means the derivative of that order. In this case y^(m) means
\frac{d^my}{dx^m}

Start by calculating y' (same as dy/dx), y'' (same as d²y/dx²), and so on.

 

[priscilla98]

y^m doesn't lead to any of the choices given, but y^(m) does for one value of m. The notation of an exponent in parentheses usually means the derivative of that order. In this case y^(m) means
\frac{d^my}{dx^m}

Start by calculating y' (same as dy/dx), y'' (same as d²y/dx²), and so on.

By using dy/dx for y = x^-3 + x, would it be this below

dy d d
--- = --- (x^-3) + --- (x)
dx dx dx

 

[Mark44]

Start with y = x^-3 + x
Find y'.
Find y''.
Find y'''.

Are you having trouble differentiating the expression in the first equation above?