Find the derivative of the function

Question

Find the derivative of the function y = arctanX + X/ 1+X²

Answer 1

This is a trick question, and thus Raymond B.'s solution is incorrect. Since division has higher precedence than addition, we have:

y = arctanX + X/ 1+X² = arctan(X) + (X/1) + X²

...and thus the derivative is:

y' = 1/(1+X²) + 1 + 2X

Answer 2

y'=

dy/dx= 2/(x^2+1)^2

y=arctanx +x/(1+x)

y'= (arctanx)' + [x/{x+1)]'

y'= 1/(x^2+1) +(1-x^2)/(x^2+1)^2

y'= 1/(x+1)-2x^2/(x+1)^2

y'= 2/(x^2+1)^2