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IB Mathematics: Applications and Interpretation HL · AHL 2: Further Derivatives · AHL 2.1

Differentiating powers, trig, e^x and ln x Problem set B Answers

Skills

    1. (a) \(f'(x)=\frac{7}{4}x^{3/4}\)
    2. (b) \(f'(x)=-6x^{-7/5}\)
    1. (a) \(f'(x)=\frac{8}{5}x^{-4/5}\)
    2. (b) \(f'(x)=\frac{14}{3}x^{-4/3}\)
    1. (a) \(\frac{dy}{dx}=15x^{1/2} - \frac{9}{2}x^{-5/2}\)
    2. (b) \(\frac{dy}{dx}=-3x^{-4/3} + \frac{8}{3}x^{-1/3}\)
    1. (a) \(f'(x)=4\cos x - 7\sin x\)
    2. (b) \(f'(x)=\frac{1}{4}\cos x + 5\sin x\)
    1. (a) \(f'(x)=-\frac{6}{\cos^2 x}\)
    2. (b) \(f'(x)=3x^{2} + \frac{1}{\cos^2 x}\)
    1. (a) \(y'=\frac{8}{x}\)
    2. (b) \(y'=-\frac{3}{x} + 5e^x\)
    1. (a) \(y'=\frac{15}{x}\)
    2. (b) \(y'=\frac{8}{x}\)

In context

    1. (a) \(\frac{dV}{dt}=18t^{1/2}\)
    2. (b) 54 litres per minute
    1. (a) \(\frac{dT}{dt}=12\cos t + 9\sin t\)
    2. (b) 9.83 degrees per minute
    1. (a) \(\frac{dx}{d\theta}=\frac{40}{\cos^2 \theta}\)
    2. (b) 68.4 cm per radian
    1. (a) \(N=30 + 16\ln w;\ \frac{dN}{dw}=\frac{16}{w}\)
    2. (b) 3.2 hundred fish per week

Stretch

    1. (a) \(f'(x)=\frac{3}{2}x^{1/2} - 6x^{-1/2}\)
    2. (b) x = 4
    1. (a) \(\frac{dy}{dx}=e^x - \frac{6}{x}\)
    2. (b) x = 1.43

jmaths.xyz · AI HL · AHL 2.1 Differentiating powers, trig, e^x and ln x