`y = sqrt(x) + (1/4)(sin(2x)^2)` Find the derivative of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the derivative of the function, hence you need to use the chain rule, where it is required, such that:

`y' = (sqrt x)' + (1/4)*(sin (2x)^2)'*((2x)^2)'*(2x)'`

`y' = 1/(2(sqrt x)) + (1/4)*(cos (2x)^2)*(2*(2x))*2`

`y'= 1/(2(sqrt x)) + (8/4)*x*(cos (2x)^2)`

`y'= 1/(2(sqrt x)) + 2x*(cos (2x)^2)`

Hence, evaluating the derivative of the function, yields `y'= 1/(2(sqrt x)) + 2x*(cos (2x)^2).`