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<6πShow that
dydx=ax2+b \frac{dy}{dx} = \frac{a}{x^2 + b} dxdy=x2+bawhere a a\,a and b b\,b are integers to be determined.
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.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
