Calculus: Early Transcendentals, Chapter 3, 3.6, Section 3.6, Problem 21

Given y=2*x*log10(sqrt(x)) we wish to find y'(x).
Write y into separate functions as follows:
let f(x)=2*x, g(x)=log10(x), w(x)=sqrt(x).
Use the Chain rule: d/dx F(G(x))= F'(G(x)) * G'(x)
and the Product rule: d/dx (F(x)G(x)) = F'(x)G(x) + F(x)*G'(x)
Compute f'(x), g'(x) and w'(x) ,
f'(x)=2.
Note that g(x)=log10(x)=ln(x)/ln(10)=1/ln(10) * ln(x)
so that g'(x) = 1/ln(10) * 1/x.
w'(x) = 1/(2*sqrt(x)).
Now apply the Chain rule and product rule:
y'(x) = 2*log10(sqrt(x)) + 2*x*1/ln(10)*1/sqrt(x)*1/(2*sqrt(x))
Combine like terms,
y'(x) = log10(x) + 1/ln(10) = (ln(x)+1)/ln(10)