Question

find y' using implicit differentiation: cosx+y^1/2=4

Answer 1

implicit differentiation wrt x: treat every y as an unknown function y(x).

this means that you always use the chain rule:

answer is:

\[-\sin(x) + (1/2)y^{-\frac{ 1 }{ 2 }}*y' = 4\]
to find y', isolate it. in this case it's rather simple:
\[y' = \frac{ 4 + sinx }{ (1/2)y^{-\frac{ 1}{ 2 } }} = (8 + 2sinx)\sqrt{y}\]

Answer 2

this is incorrect

Answer 3

what is the correct answer?