Question

radical (3x+y)=3+x^2y^2 find y' using implicit differentiation formula

Answer 1

Which part do you need help differentiating?

Answer 2

\[\frac{d}{dx}(x^2y^2) \text{ Note: Requires product rule }\]

Answer 3

oh it is \[\sqrt{3x+y}=3+x^2y^2 \\ \text{ Honestly I don't like \square roots so I'm going \to \square both sides } \\ 3x+y=(3+x^2y^2)^2\]

Answer 4

1/2 radical(3x+y)(4+y') =2x^2.y.y' +2xy^2

Answer 5

But we could also do it your way...

Answer 6

except we need to use chain rule on the left hand side

Answer 7

yeah, it's very hard to write here

Answer 8

\[\frac{1}{2 \sqrt{3x+y}} \cdot (3+y')=2xy^2 +2yy'x^2 \]
\[\frac{3}{2 \sqrt{3x+y}}+\frac{y'}{2 \sqrt{3x+y}}=2xy^2 +2yy'x^2 \]

Answer 9

next step is to gather your y' parts together

Answer 10

i don't know what you did on the right side

Answer 11

distribute?

Answer 12

a(b+c)=ab+ac

Answer 13

or
(b+c)a=ab+ac