Respuesta :

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]