Answer
a. $y = 2x$
b. Graph
Work Step by Step
$y = 2xsinx$
Use the product rule:
$y' = \frac{d(2x)}{dx} \times + 2x \times \frac{d(sinx)}{dx}$
$y' = 2sinx + 2xcosx$
Now plug $\frac{\pi}{2}$:
$y' = 2sin(\frac{\pi}{2}) + 2(\frac{\pi}{2})cos(\frac{\pi}{2})$
$y' = 2 + 0$
$y' = 2$
With this answer we can find the equation of the tangent line:
$y = m(x - x_{1}) + y_{1}$
$y = 2(x -\frac{\pi}{2}) + \pi$
$y = 2x -\pi + \pi$
$y = 2x$
b. To draw this graph, draw the equation of the tangent line $(y = 2x)$ and original function $(y = 2xsinx)$
