ANSWER
g'(0.1) = 4
EXPLANATION
As stated, g(x) is a composition of two functions: f(x) and 2x. To find its derivative, we have to use the chain rule,
[tex]g^{\prime}(x)=f^{\prime}(x)\cdot(2x)^{\prime}=f^{\prime}(2x)\cdot2[/tex]
So, the derivative of g(x) = f(2x) is twice the derivative of f(x) and, therefore,
[tex]g^{\prime}(0.1)=f^{\prime}(2\cdot0.1)\cdot2=f^{\prime}(0.2)\cdot2=2\cdot2=4[/tex]
Hence, g'(0.1) = 4.
