Please simplify all answers completely and show ALL steps an

Show all work simplify all answers completely 1. (5 pts) Find the second derivative of g x) Vx2 16.

Solution

given g(x)=(x²+16)

g(x)=(x²+16)^1/2

differentiate with respect to x . d_/dx (f(x))ⁿ =n(f(x))^n-1(f \'(x))

g\'(x)=(1_/2)(x²+16)^(1/2)-1(2x^2-1+0)

g\'(x)=(1_/2)(x²+16)^(-1/2)(2x)

g\'(x)=x(x²+16)^(-1/2)

differentiate with respect to x . product rule:(uv)\'=u\'v +uv\'

g\'\'(x)=[1*(x²+16)^(-1/2)]+[x(-1_/2)(x²+16)^(-1/2)-1(2x+0)]

g\'\'(x)=[(x²+16)^(-1/2)]+[x(-1_/2)(x²+16)^(-3/2)(2x)]

g\'\'(x)=[(x²+16)^(-1/2)]-[x²(x²+16)^(-3/2)]

g\'\'(x)=[1_/(x²+16)]-[x²_{/(x²+16)(x²+16)}]

g\'\'(x)=[(x²+16)-x²]_{/(x²+16)(x²+16)}

g\'\'(x)=16_{/(x²+16)(x²+16)}

g\'\'(x)=16_{/(x²+16)^3/2}