find xy help

Question

By applying implicit differentiation, find y'(x) below.

 

y√(x^2+y^2 )=15

Answer 1

Get rid of the square root sign by squaring both sides

 

x^2y +  y^3 = 225

 

Now the differentiation part

 

2xy + x^2y' + 3y^2 y' = 0

 

y' ( x^2 + 3y^2) = -2xy

 

y' = -2xy / (x^2 + 3y^2)

 

That's your answer