Question

implicit derivation of x + ln(y) = x^2*y^3

Answer 1

I got as far as \[1+ y'(x)/y=3x ^{2}y ^{2}y'(x)+2xy ^{3}\]

Answer 2

still here?

Answer 3

it's just algebra from here out solving for y'\[1+\frac {y'}y=3x^2y^2y'+2xy^3\]\[y+y'=3x^2(y')^2+2xy^3\]\[3x^2(y')^2-y'+2xy^3=0\]\[y'={1\pm\sqrt{1+4(3x^2)(2xy^3)}\over6x^2}={1\pm\sqrt{1+24x^3y^3}\over6x^2}\]

Answer 4

ah thank you