2.4: Logarithmic differentiation and small increments

0606/21/M/J/17 — Question 3 · 4 marks

The variables xx and yy are such that y=ln⁡(x2+1)y = \ln(x^{2} + 1).
(i)
Find an expression for dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}.
[2]
(ii)
Hence, find the approximate change in yy when xx increases from 33 to 3+h3 + h, where hh is small.
[2]