Find g(f(x)) f(x)=3x^2 , g(x)=2x^3

$f (x) = 3 x^{2}$ , $g (x) = 2 x^{3}$

Set up the composite result function.

$g (f (x))$

Evaluate $g (3 x^{2})$ by substituting in the value of $f$ into $g$ .

$g (3 x^{2}) = 2 {(3 x^{2})}^{3}$

Apply the product rule to $3 x^{2}$ .

$g (3 x^{2}) = 2 (3^{3} {(x^{2})}^{3})$

Raise $3$ to the power of $3$ .

$g (3 x^{2}) = 2 (27 {(x^{2})}^{3})$

Multiply the exponents in ${(x^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$g (3 x^{2}) = 2 (27 x^{2 \cdot 3})$

Multiply $2$ by $3$ .

$g (3 x^{2}) = 2 (27 x^{6})$

Multiply $27$ by $2$ .

$g (3 x^{2}) = 54 x^{6}$