Implicit Differentiation Question

Question

Consider the following:

 

cos(x)+√y = 5

 

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). 

 

Help!?

Answer 1

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

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

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

y' = 2 sin x * sqrt(y)



-------------------

cos x + sqrt(y) = 5

sqrt(y) = 5 - cosx

y = 25 - 10cosx + cos^2

y' = 10sinx -2 cosx sinx

= 2sinx ( 5 -cos) =

2 sinx * sqrt(y)