Answer:
[tex]\frac{dy}{dx}\ = tanx + x *sec^{2}x[/tex]
Step-by-step explanation:
[tex]y=xtanx[/tex]
Differentiate with respect to x by using product rule .
[tex]y=xtanx\\\\\frac{dy}{dx}\ = tanx * \frac{dx}{dx}\ + x * \frac{d(tanx\ )}{dx} \\As\ \ [\frac{d(tanx)}{dx} =\frac{1}{sec^{2}x } \ ]\ so\\\\\\\\\[/tex]
[tex]\frac{dy}{dx}\ = tanx + x * \frac{1}{cos^{2}x \ } \\\frac{dy}{dx}\ = tanx + x *sec^{2}x[/tex]