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

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:



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



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





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) 




So we get our equation:



So our answer is E

Feel free to ask any questions.
Hopes this helps!

Answerresponsibility law;