The depth of water in an experimental filtration vessel, D D\,D centimetres, varies according to the radius of the sediment layer r r\,r millimetres, such that D=(2r3+9r2)4D = (2r^3 + 9r^2)^4D=(2r3+9r2)4. Determine the rate of change of the depth with respect to the radius, dDdr\displaystyle \frac{dD}{dr}drdD.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, 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). Each one has a worked solution and a mark scheme showing where the marks go.