x^3 y + y^3 x = 30 derivative

JayBird221

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I need to find the y' from x^3*y + y^3*x = 30
I'm not sure how to finish this. I know it's an implicit function but I'm not sure how to do it.

I reach to a conclusion I need to do two calculation first for the x^3*y and the y^3*x
and I think I can use the u*v' + u'*v formula for both of them but I'm not sure if it's correct.
So I tried to calculate it and I wonder if it's correct
x^3 y
3x^*12 y + x^3*1

is the derivative above correct or is there any special treatment I need to do?
Thanks for the help
 
I need to find the y' from x^3*y + y^3*x = 30
I'm not sure how to finish this. I know it's an implicit function but I'm not sure how to do it.

I reach to a conclusion I need to do two calculation first for the x^3*y and the y^3*x
and I think I can use the u*v' + u'*v formula for both of them but I'm not sure if it's correct.
So I tried to calculate it and I wonder if it's correct
x^3 y
3x^*12 y + x^3*1

is the derivative above correct or is there any special treatment I need to do?
Thanks for the help

Your general path is correct - but details are not.

x^3*y + y^3*x = 30

differentiating we get:

[3*x^2 * y + x^3 * y'] + [y^3 + x * 3 * y^2 * y'] = 0

Now collect all the terms with y' as a factor and continue.....
 
Your general path is correct - but details are not.

x^3*y + y^3*x = 30

differentiating we get:

[3*x^2 * y + x^3 * y'] + [y^3 + x * 3 * y^2 * y'] = 0

Now collect all the terms with y' as a factor and continue.....

Thanks a lot for your help! Also with your explanation I understand it more!
Once again Thank you!
 
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