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 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.
