Consider the following.

Question

cos(x) + sqrt(y)= 1

(a) Find y' by implicit differentiation.
y' = 2y^(1/2) sin(x)
Correct: Your answer is correct.

(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.
y' = ?

(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).
y' =?

Answer 1

I did this for you here:
https://www.jiskha.com/display.cgi?id=1526060796

Why are you reposting it ?

Answer 2

It wasn't correct and I wanted to post my answer I got for context

Answer 3

But it is correct.
Proof:
http://www.wolframalpha.com/input/?i=find+dy%2Fdx+for+cos(x)+%2B+sqrt(y)%3D+1

Answer 4

cos(x) + sqrt(y)= 1
-sin x dx/dx + (1/2) y^-.5 dy/dx = 0
dy/dx = 2 sin x /y^-.5 = 2 sin x sqrt y
so it is surely correct
cos(x) + sqrt(y)= 1

sqrt y = 1 - cos x
y = 1 -2 cos x + cos^2 x
dy/dx = 2 sin x - 2 cos x sin x = 2 sin x (1- cos x) That is part 2
but we know that 1 - cos x = sqrt y
so
dy/dx = 2 sin x sqrt y (again)
that shows they are consistent