Determine ddxln(sec43x)\frac{d}{dx}\ln(\sec^4 3x)dxdln(sec43x), giving your answer in its simplest form.
Differentiate (3x2−4)3(3x^2 - 4)^3(3x2−4)3 with respect to xxx.
Hence show that
∫02x(3x2−4)2 dx=K \int_{0}^{2} x(3x^2 - 4)^2 \, dx = K ∫02x(3x2−4)2dx=Kwhere KKK is an integer to be found.
(Solutions relying on calculator technology are not acceptable.)
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.
