UPSC NDA Math Model Paper 2

Given curve is y = 2x sin x
Taking derivative on both side, we get

dy

dx

=2x‌cos‌x+2‌sin‌x
Put x=

π

2

to find the equation of tangent at the point (

π

2

,π).

dy

dx

=2

π

2

‌cos‌

π

2

+2‌sin‌

π

2

dy

dx

=2
The equation of tangent at point (x1,y1) with slope m is given by
(y−y1)=m(x−x1)
(y−π)=2(x−

π

2

)
y=2x
Hence, the equation of the tangent line to the curve y=2x‌sin‌x at the point (

π

2

,π) is 2x.