Differentiate the function y = 2x*log[10] (sqrt (x))

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)