Derivative of y=x³/x²+1

1. Differentiate $\frac{x^{3}}{x^{2}} + 1$ term by term:

   1. Apply the quotient rule, which is:

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

      $f{\left(x \right)} = x^{3}$ and $g{\left(x \right)} = x^{2}$.

      To find $\frac{d}{d x} f{\left(x \right)}$:

      1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

      To find $\frac{d}{d x} g{\left(x \right)}$:

      1. Apply the power rule: $x^{2}$ goes to $2 x$

      Now plug in to the quotient rule:

      $1$

   2. The derivative of the constant $1$ is zero.

   The result is: $1$

The answer is:

$$1$$