# How do you differentiate y=sqrt(x + 1)/root3( x^4) ?

$\frac{3 {\left(x + 1\right)}^{- \frac{1}{2}} \cdot {x}^{\frac{4}{3}} - 8 {\left(x + 1\right)}^{\frac{1}{2}} \cdot {x}^{\frac{1}{3}}}{6 {x}^{\frac{8}{3}}}$
$\frac{\frac{1}{2} \cdot {\left(x + 1\right)}^{- \frac{1}{2}} \cdot {x}^{\frac{4}{3}} - 2 {\left(x + 1\right)}^{\frac{1}{2}} \cdot \frac{4}{3} \cdot {x}^{\frac{1}{3}}}{x} ^ \left(\frac{8}{3}\right)$
Multiplying numerator and denominator by $6$
$\frac{3 {\left(x + 1\right)}^{- \frac{1}{2}} \cdot {x}^{\frac{4}{3}} - 8 {\left(x + 1\right)}^{\frac{1}{2}} \cdot {x}^{\frac{1}{3}}}{6 \cdot {x}^{\frac{8}{3}}}$