Question 260674
Substitute

{{{u=5x^3 + 7x}}}
{{{y=u^(1/4)}}}
Then the chain rule, 
{{{dy/dx=(dy/du)(du/dx)}}}
{{{dy/du=(1/4)u^(-3/4)}}}
{{{du/dx=15x^2+7}}}
{{{dy/dx=(1/4)(15x^2+7)/(5x^3+7x)^(3/4)}}}
You have a mistake on the exponent of 15x^2 in the numerator.
I think that's as reduced as possible.