Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 16

Differentiate $\displaystyle y = x^2 \sin x \tan x$


$
\begin{equation}
\begin{aligned}

y' =& (x^2 \sin x) \frac{d}{dx} (\tan x) + (\tan x) \frac{d}{dx} (x^2 \sin x)
&& \text{Using Product Rule}
\\
\\
y' =& (x^2 \sin x) (\sec^2 x) + (\tan x) (x^2 \cos x + 2x \sin x)
&& \text{Simplify the equation}
\\
\\
y' =& x^2 \sin x \sec^2 x + x^2 \cos x \tan x + 2 x \sin x \tan x
&& \text{Combine like terms}
\\
\\
y' =& x^2 \sin x \sec^2 x + x^2 \sin x + 2x \sin x \tan x
&& \text{Factor out}
\\
\\
y' =& x \sin x (x \sec ^2 x + x + 2 \tan x)
&& \text{}


\end{aligned}
\end{equation}
$