X^3 - xy + y^3= 1

Solve for dy/dx

Question

X^3 - xy + y^3= 1 

Solve for dy/dx

unklerhaukus · Answer

take the derivative term by term,

what is the derivative (with respect to x)   of x^3

unklerhaukus · Answer

d/dx (x^3) = ?

unklerhaukus · Answer

[for the second two terms you will need to apply the product rule]

anonymous · Answer

i have 3x^2 - x (dy/dx) + 3y^2 dy/dx = 0

unklerhaukus · Answer

youv'e missed a term,

d/dx (xy)  =x d/dx (y) + y d/dx (x)

anonymous · Answer

ok back up is it 
3x^2 - (x dy/dx + y + 1) = 3y^2 dy/dx =0

anonymous · Answer

3x^2 - (x dy/dx + y dy/dx x ) + 3y^2 dy/dx =0

anonymous · Answer

am I on the right track

unklerhaukus · Answer

*
3x^2 - (x dy/dx + y d/dx (x) ) + 3y^2 dy/dx =0

unklerhaukus · Answer

that term  y d/dx (x) = y dx/dx = y (1) = y

unklerhaukus · Answer

the other terms you have done correctly

unklerhaukus · Answer

can you see what i mean?

anonymous · Answer

yea but where do I go next

unklerhaukus · Answer

3x^2 - (x dy/dx + y) + 3y^2 dy/dx =0

now you just have to solve the equation for dy/dx by rearranging

unklerhaukus · Answer

you should end up with   dy/dx = some fraction

anonymous · Answer

i am really confused on the algebra piece of it

unklerhaukus · Answer

well expand the bracket, (bring the minus across those two terms)

unklerhaukus · Answer

tell me what you get after this step

anonymous · Answer

3x

anonymous · Answer

3x^2 - x dy/dx -y +3y^2dy/dx

anonymous · Answer

sorry didn't realize I forgot to paste

unklerhaukus · Answer

dont forget the  equals sign

anonymous · Answer

of course

unklerhaukus · Answer

3x^2 - x dy/dx -y +3y^2dy/dx = 0 

now think of the dy/dx as just a variable

factor the dy/dx from two terms

anonymous · Answer

^

anonymous · Answer

oops 3x^2 - y dy/dx ( x + 3y^2) =0

unklerhaukus · Answer

not quite

anonymous · Answer

dy/dx = (-3x^2 + y) / (x + 3y^2) = 0

anonymous · Answer

dy/dx = x/y

unklerhaukus · Answer

hmm i'm not sure how you got that but its good,

except this time it dosent equal zero

anonymous · Answer

oops didn't mean to put that  lol

unklerhaukus · Answer

dy/dx cannot be simplified to x/y,  because d is not a number that can cancel, it is an operator

anonymous · Answer

ugh what am i doing wrong

anonymous · Answer

did I have it right before I tried to simply it

unklerhaukus · Answer

3x^2 - x dy/dx -y +3y^2dy/dx = 0 

3x^2-y + dy/dx (-x + 3y^2) = 0

dy/dx (-x+3y^2) = y-3x^2

dy/dx = (y-3x^2) / (-x + 3y^2)

          = (3x^2 -y ) / (x-3y^2)

anonymous · Answer

thanks I don't know what I did wrong