Which way is correct?

[Protijay]

Alright, so I am a thirteen year old trying to learn calculus (because what else am I going to do over summer. Hang out with friends? Don't be ridiculous.) Now, since I do not have access to a teacher (Because it's summer), I have been limited to the resources provided by the internet. And while they have been incredibly useful in helping me in my incredibly new efforts to learn calculus, there has been several contradictions. One of which has brought me to the point of asking for assistance.

Now, I'm doing the simple equation of 3z^7 - 7z^3 + 21x^2 . Isn't hard to do, the answer I got was 21z^6 - 21z^2 + 42z. Symbolab agrees with me on that one (it's a math site that gives you the steps to get to the answer). However, tkiryl (a site to give you math questions and the solutions) disagrees. Apparently I am supposed to apply the power rule twice (unless there's like a different name and I am just oblivious to it.) Which would give me an answer of 126z^5 - 42z + 42. Now as you can imagine, as a not-the-sharpest-tool-in-the-shed thirteen year old who can't get google to help him, I do not have any idea what is going on.

Any help is appreciated.

 

[Steven G]

Alright, so I am a thirteen year old trying to learn calculus (because what else am I going to do over summer. Hang out with friends? Don't be ridiculous.) Now, since I do not have access to a teacher (Because it's summer), I have been limited to the resources provided by the internet. And while they have been incredibly useful in helping me in my incredibly new efforts to learn calculus, there has been several contradictions. One of which has brought me to the point of asking for assistance.

Now, I'm doing the simple equation of 3z^7 - 7z^3 + 21x^2 . Isn't hard to do, the answer I got was 21z^6 - 21z^2 + 42z. Symbolab agrees with me on that one (it's a math site that gives you the steps to get to the answer). However, tkiryl (a site to give you math questions and the solutions) disagrees. Apparently I am supposed to apply the power rule twice (unless there's like a different name and I am just oblivious to it.) Which would give me an answer of 126z^5 - 42z + 42. Now as you can imagine, as a not-the-sharpest-tool-in-the-shed thirteen year old who can't get google to help him, I do not have any idea what is going on.

Any help is appreciated.

The problem I see is with your notation or rather lack of notation. You say that you have an equation 3z^7 - 7z^3 + 21z^2 and the answer is 21z^6 - 21z^2 + 42z. The problem is that you never stated a problem. For your answer to be correct you need to say that the derivative of 3z^7 - 7z^3 + 21z^2 is 21z^6 - 21z^2 + 42z. It would be best to state the problem as: If f(z) = 3z^7 - 7z^3 + 21z^2, find f'(z). The answer would then be f'(z) = 21z^6 - 21z^2 + 42z. If on the other hand they asked you to find f''(z), the the answer would be f''(z) = 126z^5 - 42z + 42.
In case you do not know, f"(z) means to compute the derivative of f(z) twice or the derivative of f'(z) once.

 

[HallsofIvy]

Alright, so I am a thirteen year old trying to learn calculus (because what else am I going to do over summer. Hang out with friends? Don't be ridiculous.) Now, since I do not have access to a teacher (Because it's summer), I have been limited to the resources provided by the internet. And while they have been incredibly useful in helping me in my incredibly new efforts to learn calculus, there has been several contradictions. One of which has brought me to the point of asking for assistance.

Now, I'm doing the simple equation of 3z^7 - 7z^3 + 21x^2 . Isn't hard to do, the answer I got was 21z^6 - 21z^2 + 42z.

Answer to what question? First one doesn't "do" an equation. There are a number of things one might do to an equation but that isn't an equation- there is no "=". But, in any case, what were you to do to or with that polynomial? Is that last term supposed to have variable "x" or did you mean to continue with "z"?

Please tell us what question you are trying to answer!

Symbolab agrees with me on that one (it's a math site that gives you the steps to get to the answer). However, tkiryl (a site to give you math questions and the solutions) disagrees. Apparently I am supposed to apply the power rule twice (unless there's like a different name and I am just oblivious to it.) Which would give me an answer of 126z^5 - 42z + 42. Now as you can imagine, as a not-the-sharpest-tool-in-the-shed thirteen year old who can't get google to help him, I do not have any idea what is going on.

Any help is appreciated.

 

[mmm4444bot]

… the simple e͏quation of 3z^7 - 7z^3 + 21x^2 …

3z^7 - 7z^3 + 21x^2 is not an equation. All equations contain an equals sign.

Instead, you could write, "the expression" or "the p͏olynomial". :cool:

… the answer I got was 21z^6 - 21z^2 + 42z … tkiryl … disagrees.

You already understand that your answer is correct.

Are you posting because you don't understand what happened at the tkiryl site? Please post a screen shot or URL, so we can see what you're looking at.

 

[JeffM]

Alright, so I am a thirteen year old trying to learn calculus (because what else am I going to do over summer. Hang out with friends? Don't be ridiculous.) Now, since I do not have access to a teacher (Because it's summer), I have been limited to the resources provided by the internet. And while they have been incredibly useful in helping me in my incredibly new efforts to learn calculus, there has been several contradictions. One of which has brought me to the point of asking for assistance.

Now, I'm doing the simple equation of 3z^7 - 7z^3 + 21x^2 . Isn't hard to do, the answer I got was 21z^6 - 21z^2 + 42z. Symbolab agrees with me on that one (it's a math site that gives you the steps to get to the answer). However, tkiryl (a site to give you math questions and the solutions) disagrees. Apparently I am supposed to apply the power rule twice (unless there's like a different name and I am just oblivious to it.) Which would give me an answer of 126z^5 - 42z + 42. Now as you can imagine, as a not-the-sharpest-tool-in-the-shed thirteen year old who can't get google to help him, I do not have any idea what is going on.

Any help is appreciated.

It appears that the problem was to find the first derivative of a given function. If that was the problem, you did it correctly.

It further appears that on one site, you were given the second derivative of that function. Without knowing exactly what you entered at that site and what exactly you asked the site to do, it is impossible to explain why you got the second derivative rather than the first. One plausible explanation is that the site gives both derivatives, and you missed that fact, but we can't be sure.

 

[Dr.Peterson]

Alright, so I am a thirteen year old trying to learn calculus (because what else am I going to do over summer. Hang out with friends? Don't be ridiculous.) Now, since I do not have access to a teacher (Because it's summer), I have been limited to the resources provided by the internet. And while they have been incredibly useful in helping me in my incredibly new efforts to learn calculus, there has been several contradictions. One of which has brought me to the point of asking for assistance.

Now, I'm doing the simple equation of 3z^7 - 7z^3 + 21x^2 . Isn't hard to do, the answer I got was 21z^6 - 21z^2 + 42z. Symbolab agrees with me on that one (it's a math site that gives you the steps to get to the answer). However, tkiryl (a site to give you math questions and the solutions) disagrees. Apparently I am supposed to apply the power rule twice (unless there's like a different name and I am just oblivious to it.) Which would give me an answer of 126z^5 - 42z + 42. Now as you can imagine, as a not-the-sharpest-tool-in-the-shed thirteen year old who can't get google to help him, I do not have any idea what is going on.

Any help is appreciated.

It looks like you're referring to this page: http://www.tkiryl.com/Calculus/Problems/Section 2.3-2.4/Differentiation/Differentiation.html

Note what it says at the top: "Find the first and second derivatives".

That's what they gave you.

It's really important to read the directions! Other than that, everything is fine.