(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.
425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.