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implicit differentiation

nasira372

x^2+2xy+y^2=4x
Prove dy/dx is 2/(x+y) - 1

I have shown my working in the attachment. I am stuck on the final step

help.png3.4KB

Reply 1

nuodai

You've done all the hard stuff, all you need to do now is rearrange to get

\dfrac{dy}{dx}

on its own (and simplify your answer by cancelling common factors).

Reply 2

nasira372

Original post by nuodai

You've done all the hard stuff, all you need to do now is rearrange to get

\dfrac{dy}{dx}

on its own (and simplify your answer by cancelling common factors).

So you move the 2x+2y to the other side to give dy/dx=4-2x-2y/2x+2y.

Cancelling out gives 2-x-y/x+y

This still isn't correct though...

What do I do next

Reply 3

nuodai

Original post by nasira372

Cancelling out gives 2-x-y/x+y

This still isn't correct though...

Yes it is. What makes you think it isn't?

Reply 4

ian.slater

Original post by nasira372

So you move the 2x+2y to the other side to give dy/dx=4-2x-2y/2x+2y.

Cancelling out gives 2-x-y/x+y

This still isn't correct though...

What do I do next

If your book shows you the answer, you might compare what you have and ask 'what do I have to do to change my answer into theirs?'

Reply 5

nasira372

Original post by nuodai

Yes it is. What makes you think it isn't?

I get 2-x-y/x+y

I need the final answer to be 2/x+y -1

What do I do to my answer to get the required answer

Reply 6

nuodai

Original post by nasira372

I get 2-x-y/x+y

I need the final answer to be 2/x+y -1

What do I do to my answer to get the required answer

Oh; well they're the same thing. Note that you can write

2-x-y

2-(x+y)

if you want to rearrange it.

Reply 7

TenOfThem

Original post by nuodai

Oh; well they're the same thing. Note that you can write

2-x-y

2-(x+y)

if you want to rearrange it.

From this line

2x + 2y + dy/dx(2x +2y) = 4

You could have seen

2(x + y)(1 + dy/dx) = 4

1 + dy/dx = 2/(x+y)

dy/dx = 2/(x+y) - 1

Reply 8

nasira372

Original post by TenOfThem

From this line

2x + 2y + dy/dx(2x +2y) = 4

You could have seen

2(x + y)(1 + dy/dx) = 4

TBH, I still dont see it even though you've pointed it out to me. The sudden appearance of the 1 is very confusing. I'd still get 3/4 marks though for what I did. Just not the final step :frown: