(i) The curve CCC has equation y=g(x)y = \text{g}(x)y=g(x) where
g(x)=e2xsec3x,−π6<x<π6 \text{g}(x) = \text{e}^{2x} \sec 3x, \quad -\frac{\pi}{6} < x < \frac{\pi}{6} g(x)=e2xsec3x,−6π<x<6πFind g′(x)\text{g}'(x)g′(x).
Hence find the xxx-coordinate of the stationary point of CCC.
A different curve has equation
x=ln(cosy),0<y<π2 x = \ln(\cos y), \quad 0 < y < \frac{\pi}{2} x=ln(cosy),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.
717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.