Would somebody mind checking my work?

The equation x^2y+2xy^3=8 defines y as a function of x, y=f(x), near x=2, y =1. Find the slope of the curve x^2y+2xy^3=8 when x=2, y=1

Question

Would somebody mind checking my work?

The equation x^2y+2xy^3=8 defines y as a function of x, y=f(x), near x=2, y =1. Find the slope of the curve x^2y+2xy^3=8 when x=2, y=1

baldymcgee6 · Answer

Here is my work

anonymous · Answer

Double check the denominator of the final line.

baldymcgee6 · Answer

oops, thank you for noticing that, forgot to square the first 2 in the denominator.
is everything else right?

anonymous · Answer

I think so. I'm going through it one more time to be sure.

anonymous · Answer

-3/8.

baldymcgee6 · Answer

Sorry, meant to type -6/16 or -3/8

anonymous · Answer

Everything else is fine.
Final line:
$$\large \frac{-2(2)(1)-2(1)^3}{2^2+6(2)(1)^2}=\frac{-3}{8}$$

baldymcgee6 · Answer

Thanks so much @CliffSedge

anonymous · Answer

Hey, my pleasure. That was all very clear and easy to check!