Calculus

Consider the following.
cos(x) + sqrt(y)= 1

(a) Find y' by implicit differentiation.
y' = 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' =?

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  1. I hope for a) you had
    -sinx + (1/2)y^(-1/2) dy/dx = 0
    dy/dx = 2√y sinx

    b) from the original:
    √y = 1 - cosx
    square both sides
    y = 1 - 2cosx + cos^2 x
    dy/dx = 2sinx + 2cosx(-sinx)
    = 2sinx(1 - cosx) , but 1-cosx = √y
    = 2sinx √y , which matches my other dy/dx

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