How do you differentiate sqrt(cos(x^2+2))+sqrt(cos^2x+2)?

1 Answer
Apr 18, 2018

(dy)/(dx)= (xsen(x^2+2)+sen(x+2))/(sqrtcos(x^2+2)+sqrt(cos^2(x+2)))

Explanation:

(dy)/(dx)= 1/(2sqrtcos(x^2+2)+sqrt(cos^2(x+2))) *sen(x^2+2)*2x+2sen(x+2)

(dy)/(dx)= (2xsen(x^2+2)+2sen(x+2))/(2sqrtcos(x^2+2)+sqrt(cos^2(x+2)))

(dy)/(dx)= (cancel2(xsen(x^2+2)+sen(x+2)))/(cancel2sqrtcos(x^2+2)+sqrt(cos^2(x+2)))

(dy)/(dx)= (xsen(x^2+2)+sen(x+2))/(sqrtcos(x^2+2)+sqrt(cos^2(x+2)))