Question #161a5

1 Answer
Feb 7, 2018

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)))