Additional Mathematics 0606 / Calculus — Differentiation 2 / 2.102.10: Quotient rule and small change for a logarithmic ratio0606/21/M/J/19 — Question 2 · 5 marksMark as done · Save for later · Show all solutionsTwo variables xxx and yyy are such that y=lnxx3y = \dfrac{\ln x}{x^{3}}y=x3lnx for x>0x > 0x>0.(i)Show that dydx=1−3lnxx4\dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{1 - 3\ln x}{x^{4}}dxdy=x41−3lnx.[3]▸ Answer(ii)Hence find the approximate change in yyy as xxx increases from e\mathrm{e}e to e+h\mathrm{e} + he+h, where hhh is small.[2]▸ Answer▸ Official mark scheme← 1.37: Cosine curve intersecting a horizontal line2.40: Quotient rule with logarithmic denominator →
