# How do you use the quotient rule to find the derivative of y=x^3/(1+x^2) ?

Jul 28, 2014

$y ' = \frac{3 {x}^{2} + {x}^{4}}{1 + {x}^{2}} ^ 2$

Explanation

Suppose,

$y = f \frac{x}{g} \left(x\right)$

Using Quotient Rule, which is

$y ' = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g \left(x\right)} ^ 2$

Similarly, following for problem

$y ' = \frac{3 {x}^{2} \left(1 + {x}^{2}\right) - {x}^{3} \left(2 x\right)}{1 + {x}^{2}} ^ 2$

$y ' = \frac{3 {x}^{2} + 3 {x}^{4} - 2 {x}^{4}}{1 + {x}^{2}} ^ 2$

$y ' = \frac{3 {x}^{2} + {x}^{4}}{1 + {x}^{2}} ^ 2$