Find dy/dx if x^2*y^3-x^3*y^2=0
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Answer ( ◜‿◝ )♡
x
3
+y
3
=3axy
Differentiating w.r.t. x, we get,
⇒3x
2
+3y
2
dx
dy
=3a[x
dx
dy
+y]
⇒3x
2
+3y
2
dx
dy
=3ax
dx
dy
+3ay
⇒(3y
2
−3ax)
dx
dy
=3ay−3x
2
⇒3(y
2
−ax)
dx
dy
=3(ay−x
2
)
⇒
dx
dy
=
y
2
−ax
ay−x
2
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