Calculus: Differentiation question using the Composite Rule.?

Question

Part (A):
Use the Composite Rule to differentiate the function
g(x) = SQRT(1+x^2)

Part(B):
Use the Composite Rule and your answer to part(A) to show that the function
h(x)=ln{x+SQRT(1+x^2)} has derivative
h'(x)=1/SQRT(1+x^2)

Right I think the answer to part(A) is g'(x)=x/SQRT(1+x^2), am I right??
But I can't figure out part(B) does anyone know how to do that part using the answer to part(A)??

Answer 1

Part (A):
g(x) = SQRT(1+x^2)
g'(x) = (1/2) (1+x^2)^(-1/2) (2x)
g'(x) = x/(1+x^2)^(1/2) or x/SQRT(1+x^2)

Part (B):
h(x)=ln{x+SQRT(1+x^2)}
h(x)=ln{x+g(x)}
h'(x)=(1/x+g(x)) (1+(x/(1+x^2)^(1/2)))
h'(x)= (1+x^2)^(-1/2)
h'(x)=1/SQRT(1+x^2) (Proven)

Answer 2

g(x)=(1+x^2)^(1/2)
g'(x)=1/2(1+x^2)^(-1/2)*d(1+x^2)
g'(x)=1/2(1+x^2)^(-1/2)*(2x)
simplify
g'(x)=x/((1+x^2)^1/2)