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)))#