#### Answer

$f'(x) = 12x^3 + 7$

#### Work Step by Step

$f(x) = 3x^4 + 7x$
$f'(x) = (3x^4 + 7x)' = (3x^4)' + ( 7x)'$
$(3x^4)' = 3 \times (x^4)' $
$(x^4)' = 4x^3 $
therefore
$(3x^4)' = 3 \times (x^4)' = 12x^3$
$(7x)' = 7 \times (x)' $
$(x)' = 1x^0 = 1$
therefore
$(7x)' = 7 \times (x)' = 7$
Therefore
$f'(x) = (3x^4 + 7x)' = (3x^4)' + ( 7x)' = 12x^3 + 7$