Question

How do you find the derivative of `y= sqrt(x^2 + cos x)` using the chain rule?

Answer 1

`y'= (2x-sinx)/(2sqrt(x^2+cosx)`

Explanation:

Given `" "y= sqrt(x^2+cosx)`
Rewrite : `" " y= (x^2+cosx)^(1/2)`

Using both power and chain rule to differentiate this function

`y'= 1/2(x^2+cosx)^(1/2 -1)*d/(dx)(x^2 + cosx)`

`=> 1/2 (x^2 + cosx)^(-1/2)*(2x-sinx)`

`=>(2x-sinx)/(2sqrt(x^2+cosx)`