The curve C C\,C has equation
x=2tan(y+π4)x∈R,−3π4<y<π4 x = 2\tan\left(y + \frac{\pi}{4}\right) \quad x \in \mathbb{R}, \quad -\frac{3\pi}{4} < y < \frac{\pi}{4} x=2tan(y+4π)x∈R,−43π<y<4πShow 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 found.
The point P P\,P with yyy-coordinate 0 lies on CCC. The tangent to C C\,C at P P\,P crosses the xxx-axis at the point QQQ. Find 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.
