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
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' =?
1 answer