Question

how do you do implicit differentiation of
sqrt (7x + y) = 9 + (x^2)(y^2)?

Answer 1

you have to take the deriavitve of both sides first

Answer 2

left hand side requires chain rule, right hand side requires product rule

Answer 3

1/2(7x+y)^(-1/2) (7 +y')= 2x y^2 + 2yx^2y'

Answer 4

lhs give
\[\frac{1}{2\sqrt{7x+y}}\times (4+y')\]

Answer 5

i mean i can do it for you, but of what benefit is that to anybody

Answer 6

i did and i ended up getting this:
\[\left(\begin{matrix}1 \\ 2\end{matrix}\right)(7x+y)^{-1/2}(7+dy/dx)=(2yx^2)(dy/dx)+(2xy^2)\]

Answer 7

i got as far as:
\[\left(\begin{matrix}7+dy/dx \\ 2\sqrt{7x+y}\end{matrix}\right)=2yx^2(dy/dx)+2xy^2\]

Answer 8

what do I do from there?

Answer 9

put dy/dx together

Answer 10

\[\left(\begin{matrix}7+dy/dx \\ 2\sqrt{7x+y}\end{matrix}\right) - 2yx^2(dy/dx)=2xy^2\]

Answer 11

do I now make a common denominator?