Answer
inside: $g(x)=x^3+2ln(x)$
outside: $f(g)=3g^{0.5}$
derivative: $\frac{df}{dx}=1.5(x^3+2ln(x)^{-0.5}*(3x^2+\frac{2}{x})$
Work Step by Step
Rewrite the function as $3(x^3+2 ln(x))^{\frac{1}{2}}$
Use the chain rule to take the derivative $\frac{d}{dx}f(g(x))=f′(g(x))g′(x)$
To find the inside, you take the number inside the parenthesis.
To find the outside, you exchange the parenthesis to a variable.
Then take its derivative and put it together.