Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 14

Take the derivative of $\displaystyle y = \frac{x^6}{x^4}$: first, use the Quotient Rule;
then, by dividing the expression before differentiating. Compare your results as a check.
By using Quotient Rule,

$
\begin{equation}
\begin{aligned}
y' &= \frac{x^4 \cdot \frac{d}{dx} (x^6) - x^6 \cdot \frac{d}{dx} (x^4) }{(x^4)^2}\\
\\
y' &= \frac{x^4 (6x^5) - x^6 (4x^3)}{x^8}\\
\\
&= \frac{6x^9 - 4x^9}{x^8}\\
\\
&= \frac{2x^9}{x^8}\\
\\
&= 2x^{9 -8}\\
\\
&= 2x
\end{aligned}
\end{equation}
$


By dividing the expression first,

$
\begin{equation}
\begin{aligned}
y &= \frac{x^6}{x^4} = x^{6 - 4} = x^2 \\
\\
y' &= \frac{d}{dx} (x^2) = 2x
\end{aligned}
\end{equation}
$


Both results agree.