Answer
\[False\]
Work Step by Step
\[\begin{gathered}
False \hfill \\
The\,\,derivative\,\,of\,\,a\,\,product\,\,is\,\,given \hfill \\
by\,\,the\,\,next\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {f\,\left( x \right)g\,\left( x \right)} \right] = f\,\left( x \right)\frac{d}{{dx}}\,\,\left[ {g\,\left( x \right)} \right] + g\,\left( x \right)\frac{d}{{dx}}\,\,\left[ {f\,\left( x \right)} \right] \hfill \\
\end{gathered} \]