3.46: Derivative of a sine product and normal

0606/21/O/N/21 — Question 3 · 9 marks

A curve has equation y=x2sin⁡x+3y = x^{2}\sin x + 3.
(a)
Show that the exact value of dydx\dfrac{\mathrm{d}y}{\mathrm{d}x} at x=π6x = \dfrac{\pi}{6} can be written as k+π12k + \dfrac{\pi}{12}, where kk is an integer.
[5]
(b)
Find the equation of the normal to the curve at the point where x=0x = 0.
[4]