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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 137

A curve C C\,C is defined by the equation

x=3tan⁡(y+π3)x∈R,−5π6<y<π6 x = 3\tan\left(y + \frac{\pi}{3}\right) \quad x \in \mathbb{R}, \quad -\frac{5\pi}{6} < y < \frac{\pi}{6} x=3tan(y+3π​)x∈R,−65π​<y<6π​
a.

Show that

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

where a a\,a and b b\,b are integers to be determined.

[4]
b.

The point P P\,P on C C\,C has yyy-coordinate −π12\displaystyle -\frac{\pi}{12}−12π​. The tangent to C C\,C at P P\,P intersects the xxx-axis at the point QQQ. Determine the exact xxx-coordinate of QQQ.

[5]
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.

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