Question

find y' if 3xy^2 + y^3=e^(x+y)

Answer 1

\[3y^2+6xyy'+3y^2y'=e^{x+y}+y'e^{(x+y)}

Answer 2

\[3y^2+6xyy'+3y^2y'=e^{x+y}+y'e^{(x+y)}\]

Answer 3

first term required the produce rule
rhs required chain rule

Answer 4

so far so good or no?

Answer 5

because it is algebra from here on in. solve for y'

Answer 6

algebra no good under sleep deprivation, lol :]
but yeah, so far makes sense

Answer 7

\[6xyy'+3y^2y'-y'e^{(x+y)}=e^{(x+y)}-3y^2\]
\[y'(6xy+3y^2-e^{(x+y)})=e^{(x+y)}-3y^2\]
\[y'=\frac{e^{(x+y)}-3y^2}{6xy+3y^2-e^{(x+y)}}\]

Answer 8

no guarantees on the algebra

Answer 9

It actually looks good, and I'm sure that's a lot more accurate than I would've produced now. Thanks again, man. Much appreciated!