Math Is Fun Forum

leadfoot

Member

Registered: 2010-11-05

Posts: 9

Diff y^5 with respect to y^2

Yes both symbols are y.

In any normal exercise things would be y with respect to x with an equation like
y = f(x) = something involving x

Following the same pattern I tried

I guess that would be too easy because the official text book answer is

Anyone know how they came up with that?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Diff y^5 with respect to y^2

hi leadfoot,

That's the right idea, but not the right substitution.

If you want to replace y^2 with x then

and

then

Do this differentiation and sub back y.

That's how they got that result.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Diff y^5 with respect to y^2

Hi leadfoot;

I am coming up with a different wrong answer. So you cannot say I copied.

I said x = y^2.

Thanks Bob! I forgot to go back with

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Diff y^5 with respect to y^2

hi bobbym

Wow! that's made my day!  I got something before you did.  I'm so happy.

:):):)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Diff y^5 with respect to y^2

You beat by more than 2 minutes and my answer was incomplete. I for got to resubstitute at the end. Good Work!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

leadfoot

Member

Registered: 2010-11-05

Posts: 9

Re: Diff y^5 with respect to y^2

thanks for the speedy solution.  I never would have thought to substitute like that although I should have known swapping directly 1 for 1 is incorrect.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Diff y^5 with respect to y^2

hi leadfoot,

You are welcome.  As you can see, bobbym and I have raced to beat each other to  your solution. 

Gosh it's such fun posting to Maths Is Fun!

:)

bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

leadfoot

Member

Registered: 2010-11-05

Posts: 9

Re: Diff y^5 with respect to y^2

I'm back.  I've tried to solve the same problem using an alternate method without all the substituting.

which happens to be the answer.  The question: is this a valid method of solving the problem or did it work out by accident?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Diff y^5 with respect to y^2

Hi leadfoot;

It seems to be working.

I am pretty sure that your idea is the same and will get the right answer here is why.If you have the problem:

You evaluate by differentiating the numerator and the denominator wrt y. Mathematically your idea is the RHS of below.

It is easy to prove equality just by multiplying the RHS by dy/dy.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.