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<π4 I(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<π2 s = \ln(5 \cos \theta), \quad 0 < \theta < \frac{\pi}{2} s=ln(5cosθ),0<θ<2πShow that
dθds=−esf(s) \frac{d\theta}{ds} = -\frac{e^s}{f(s)} dsdθ=−f(s)eswhere f(s)f(s)f(s) is a function of es e^s\,es to be determined.
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.
