we are given with the equation y = 2x*log[10](sqrt(x)) we use the rule of products of the differential equation to answer this problem. y' = u dv + v du. derivative of 2x is 2 while the derivative of log(sqrt(x)) with base 10 is 1/x ln10 * (0.5x^-0.5) in this case,
y' = 2 log[10](sqrt(x)) + 2x* 1/x ln10 * (0.5x^-0.5)
y' = 2 log[10](sqrt(x)) + l/ ln 10 sqrt(x)