# How do you differentiate y=sqrtx/(x^3+1) using the quotient rule?

##### 1 Answer
Oct 29, 2017

$\frac{1 - 5 {x}^{3}}{2 \sqrt{x} {\left({x}^{3} + 1\right)}^{2}}$

#### Explanation:

$\frac{d}{\mathrm{dx}} \left(f \frac{x}{g} \left(x\right)\right) = \frac{g \left(x\right) \cdot \frac{d}{\mathrm{dx}} f \left(x\right) - f \left(x\right) \cdot \frac{d}{\mathrm{dx}} g \left(x\right)}{g {\left(x\right)}^{2}}$ ----------->(A)

here

f(x)=$\sqrt{x}$ and
g(x)= ${x}^{3} + 1$
$\frac{d}{\mathrm{dx}} \left(\sqrt{x}\right) = \left(\frac{1}{2 \cdot \sqrt{x}}\right)$
$\frac{d}{\mathrm{dx}} \left({x}^{3} + 1\right) = 3 \cdot {x}^{2}$

Substitute the above values in equation (A) and calculate the required answer.