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

1 Answer
Dec 14, 2015

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)