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Solving Equations

The first equation differentiates into the second. How do I solve the second equation to get to the third?

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(edited 3 years ago)
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Varss
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Original post by Meggggggggggg
The first equation differentiates into the second. How do we solve the second equation to get to the third?

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Try writing all the sqr(x) in index form and split up the fraction into 3 parts
Original post by Varss
Try writing all the sqr(x) in index form and split up the fraction into 3 parts

and where would you go from here?
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Original post by Meggggggggggg
and where would you go from here?
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Simplify each term
Here’s a recap incase you’ve forgotten 18x4/39x2=2x−23\frac{18x^{4/3}}{9x^{2}} = 2x^{\frac{-2}{3}}
(edited 3 years ago)
Original post by laurawatt
Simplify each term
Here’s a recap incase you’ve forgotten 18x4/39x2=2x−23\frac{18x^{4/3}}{9x^{2}} = 2x^{\frac{-2}{3}}

This is what I did originally but i'm still confused how you get from this step to the last?
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Original post by Meggggggggggg
This is what I did originally but i'm still confused how you get from this step to the last?
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I would have taken a slightly different track initially, however going with what you have:

1) The multiplier in the middle term is incorrect - where should the "4" be?

2) What you're aiming for has a constant term, albeit inside the parentheses, but your equation's terms all involve x, so is there something you could multiply it by to get a constant term?
(edited 3 years ago)
Original post by ghostwalker
I would have taken a slightly different track initially, however going with what you have:

1) The multiplier in the middle term is incorrect - where should the "4" be?

2) What you're aiming for has a constant term, albeit inside the parentheses, but your equation's terms all involve x, so is there something you could multiply it by to get a constant term?

Is it worth restarting as I am still confused. How would you have started initially?
Original post by Meggggggggggg
Is it worth restarting as I am still confused. How would you have started initially?


Probably not worth restarting, as it will lead to the same issue as you have here. 'Can look at it afterwards, as it's only a minor variation.

In your second term the multiplier should be 1/4, not 4.

Looking at what you're aiming at, all the powers of x are positive, and there is a constant term, so what could you multiply your equation by (after correcting it), to arrive at that state?
Original post by ghostwalker
Probably not worth restarting, as it will lead to the same issue as you have here. 'Can look at it afterwards, as it's only a minor variation.

In your second term the multiplier should be 1/4, not 4.

Looking at what you're aiming at, all the powers of x are positive, and there is a constant term, so what could you multiply your equation by (after correcting it), to arrive at that state?

Ahh, thanks I have it now. I changed a random negative to a positive further up which didn't help but I got there in the end!
Original post by Meggggggggggg
Ahh, thanks I have it now. I changed a random negative to a positive further up which didn't help but I got there in the end!


Cool.

As to the variation then.

Your initial equation is in essence a fraction is equal to 0.

When is a fraction zero? When the numerator is zero.

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