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# Implicit differentiation, what am I doing wrong? watch

1. Use implicit differentiation to find dy/dx for cos(x+y) + sin(x+y) = 0.5

Differentiating this I got -sin(x+y)(1+dy/dx) + cos(x+y)(1+dy/dx) = 0

I rearranged this to get dy/dx = sin(x+y) - cos(x+y) / cos(x+y) - sin (x+y)

Then using the given equation I rearranged and got

-cos (x+y) = -0.5 +sin(x+y)
and -sin(x+y) = -0.5 + (cosx+y)
and tried subbing in my dy/dx but it gives some other expression, the answer should just be -1

where do I go from here?

Thanks
2. (Original post by DonWorryJockIsHere)
Use implicit differentiation to find dy/dx for cos(x+y) + sin(x+y) = 0.5

Differentiating this I got -sin(x+y)(1+dy/dx) + cos(x+y)(1+dy/dx) = 0
Try factorising at this point.

Edit: You don't actually need implicit differentiation for this question, and could use the sum/product trig. rules, if you've covered them.
3. (Original post by ghostwalker)
Try factorising at this point.

Edit: You don't actually need implicit differentiation for this question, and could use the sum/product trig. rules, if you've covered them.
I factorised dy/dx and made it the subject as thats what you are trying to find?
4. (Original post by DonWorryJockIsHere)
I factorised dy/dx and made it the subject as thats what you are trying to find?
Factorising where ghostwalker indicated gives you the solution you seek immediately.
5. (Original post by DonWorryJockIsHere)
Use implicit differentiation to find dy/dx for cos(x+y) + sin(x+y) = 0.5

Differentiating this I got -sin(x+y)(1+dy/dx) + cos(x+y)(1+dy/dx) = 0

I rearranged this to get dy/dx = sin(x+y) - cos(x+y) / cos(x+y) - sin (x+y)

Then using the given equation I rearranged and got

-cos (x+y) = -0.5 +sin(x+y)
and -sin(x+y) = -0.5 + (cosx+y)
and tried subbing in my dy/dx but it gives some other expression, the answer should just be -1

where do I go from here?

Thanks
The answer is a lot easier than you are trying to make it:
1.first differentiate in respect to x remembering that cos(ax+b)=-a sin(ax+b) and sin(ax+b)=a cos(ax+b) we get cos(x+y)-sin(x+y)
differentiate with respect to y because there is only one x and y, we will get the same result cos(x+y)-sin(x+y)
3.the next step is to add a minus sign and divide you answers to parts 1 and 2, which are the same giving you -1.

This method is a much simpler method of implicit differentiation that they don't seem to give in the textbooks for some reason.
6. Dalek isn't trolling in case people are suspicious. He did fail to say that you need to make the implicit equation equal to zero before using this technique.

I can't agree that this is any easier than ghostwalker's method though.
7. (Original post by Mr M)
Dalek isn't trolling in case people are suspicious. He did fail to say that you need to make the implicit equation equal to zero before using this technique.

I can't agree that this is any easier than ghostwalker's method though.
Is it just (1+dy/dx) (cos(x+y) - sin (x+y)) = 0? then you can get dy/dx = -1? but I dont see why cos (x+y) - sin (x+y) = 0?
8. (Original post by DonWorryJockIsHere)
Is it just (1+dy/dx) (cos(x+y) - sin (x+y)) = 0? then you can get dy/dx = -1? but I dont see why cos (x+y) - sin (x+y) = 0?
If ab=0, then either a=0 or b= 0 or both.

In this case

either dy/dx=-1,

or cos(x+y)=sin(x+y) in which case tan(x+y)=1, i.e is constant. So x+y is constant. I.e. x+y=c and y=c-x, and once again dy/dx = -1.

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Updated: December 30, 2012
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