(i) The altitude of a research drone HHH, measured in decameters, is modeled by the function
H(t)=e−0.4tsec0.5t,0≤t<π H(t) = \text{e}^{-0.4t} \sec 0.5t, \quad 0 \le t < \pi H(t)=e−0.4tsec0.5t,0≤t<πwhere ttt is the time in minutes after deployment.
Find H′(t)H'(t)H′(t).
Hence determine the time ttt at which the altitude of the drone is stationary.
A separate flight path is defined by the implicit relationship
x=ln(2siny),0<y<π2 x = \ln(2\sin y), \quad 0 < y < \frac{\pi}{2} x=ln(2siny),0<y<2πShow that
dydx=exf(x) \frac{\text{d}y}{\text{d}x} = \frac{\text{e}^x}{\text{f}(x)} dxdy=f(x)exwhere f(x)\text{f}(x)f(x) is a function of ex\text{e}^xex that should be found.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) 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.
