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

1 Answer
Mauricio M.
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)))#

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