Question

Question #161a5

Answer 1

`y'=- sin(x)/(2 sqrt(cos(x)))`

Explanation:

Just use the chain rule

`y=sqrt(cos(x))=(cos(x))^(1/2)`
`y'=[(cos(x))^(1/2)]^'=[cos(x)]^'\cdot (1/2)(cos(x))^(1/2-1)`
`y'=- sin(x)\cdot (1/2)\cdot (cos(x))^(-1/2)`
`y'=- sin(x)/(2 sqrt(cos(x)))`

You could use the square root rule:

`y= sqrt(cos(x))", " u=cos(x)=>du=-sin(x)`
`y= sqrt(u)=>y'=(du)/(2 sqrt(u))=(-sin(x))/(2 sqrt(cos(x)))`