Question

The equations of the tangent to the curve y=xsinx at the point (pi/2,pi/2) is

A) y=x -pi
B) y= pi/2
C)y= pi-2
D) y= x+pi/2
E) y= x

Answer 1

The first thing you have to realize is that tangent is the slope of a curve on a given point. You can solve for the slope by finding the derivative of the given function. So:

$\frac{d}{dx} xsin(x)$

Next use product rule (I recommend watching videos if you're confused):

$= [sin(x)] + [x*cos(x)]$

Next substitute you x-value (π/2) into your derivative:

$= [sin( \frac{ \pi}{2} )] +[ \frac{\pi}{2}*cos( \frac{\pi}{2})]$
$= 1 + \frac{\pi}{2} *0$
$= 1$

So our slope at π/2 is 1. Next we use our slope-form and substitute our given value and solve for y-intercept (algebra-stuff) 

$( \frac{\pi}{2}) = 1( \frac{\pi}{2}) + b$
$b = 0$

So we get our equation:

$y = x$

So our answer is E

Feel free to ask any questions.
Hopes this helps!