In a study of harmonic oscillations with variable frequency, the power P P\,P produced by a generator at time t t\,t is modeled by the equation
P=tcos(3t)t>1,P>0 P = t^{\cos(3t)} \quad t > 1, \quad P > 0 P=tcos(3t)t>1,P>0Find, by firstly taking natural logarithms, an expression for dPdt\frac{dP}{dt}dtdP in terms of ttt and PPP.
Hence show that the values of t t\,t for which the power is stationary are solutions of the equation
3tlnttan(3t)=1 3t \ln t \tan(3t) = 1 3tlnttan(3t)=1Practise 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.
