The intensity of light I I\,I at a distance w w\,w from a source is modeled by the equation I(w)=e4wsec2w,−π4<w<π4I(w) = e^{4w} \sec 2w, \quad -\frac{\pi}{4} < w < \frac{\pi}{4}I(w)=e4wsec2w,−4π<w<4π (a) Find I′(w)I'(w)I′(w). (b) Determine the www-coordinate of the stationary point for the light intensity curve.
In a separate experiment, the relationship between a signal s s\,s and a phase angle θ \theta\,θ is given by s=ln(5cosθ),0<θ<π2s = \ln(5 \cos \theta), \quad 0 < \theta < \frac{\pi}{2}s=ln(5cosθ),0<θ<2π Show that dθds=−esf(s)\frac{d\theta}{ds} = -\frac{e^s}{f(s)}dsdθ=−f(s)es where f(s)f(s)f(s) is a function of es e^s\,es to be determined.
Practise Edexcel A Level Maths 9.4 The Product Rule with exam-style questions for A Level Maths. 30 questions, 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.