3.34: Small change for a mixed trig–algebraic function

0606/23/M/J/23 — Question 7 · 6 marks

Variables xx and yy are such that y=x+4x2sinx8x3y = x + 4x^{2}\sin x - \dfrac{8}{x^{3}}. Use differentiation to find the approximate change in yy as xx increases from 0.10.1 to 0.1+h0.1 + h, where hh is small.
[6]