Implicit Differentiation problem2

Question

Consider the following.

cos x +

y

 = 4

(a) Find y' by implicit differentiation.

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

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

Answer 1

cos x + sqrt(y) = 4

-sinx + (1/2)*y^(-1/2) * y' = 0

(1/2)*y^(-1/2)*y' = sin x

y^(1/2)*y' = 2(sin x)

y' = 2(sinx)*y^(1/2)