Skip to content

Course home

3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546
Question 22

The curve C C\,C has the equation

x=2tan⁡2yx = 2\tan 2yx=2tan2y, where −π4<y<π4\displaystyle -\frac{\pi}{4} < y < \frac{\pi}{4}−4π​<y<4π​

You may use the result ddu(tan⁡ku)=ksec⁡2ku\dfrac{d}{du}(\tan ku) = k\sec^2 kudud​(tanku)=ksec2ku.

Show that, for all points (x,y)(x, y)(x,y) lying on CCC,

dydx=ax2+b\displaystyle \frac{dy}{dx} = \frac{a}{x^2 + b}dxdy​=x2+ba​

where a a\,a and b b\,b are constants to be found.

[7]
Markscheme

3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank