Differentiating powers of x Problem set A Answers

1. (a) \(f'(x)=8x^7\)
2. (b) \(h'(u)=-5u^{-6}\)
3. (c) \(\frac{ds}{dr}=-9r^{-10}\)

1. (a) \(\frac{dy}{dx}=20x^3\)
2. (b) \(g'(t)=-18t^5\)
3. (c) \(\frac{dy}{dx}=0\)
4. (d) \(\frac{dy}{dx}=-4\)

1. (a) \(\frac{dy}{dx}=-15x^{-4}\)
2. (b) \(\frac{dy}{dt}=60t^{-6}\)
3. (c) \(f'(x)=\tfrac23x^{-2}\)
4. (d) \(\frac{dy}{dx}=-\tfrac32x^{-7}\)

1. (a) \(\frac{dy}{dx}=12x^2-12x+1\)
2. (b) \(\frac{dy}{dx}=2x^4-3x^3\)
3. (c) \(f'(x)=-6x+\tfrac12x^2\)
4. (d) \(\frac{dy}{dx}=2x-3-4x^{-2}\)

1. (a) \(f'(x)=12x^2-6x\)
2. (b) \(g'(x)=2x-3\)
3. (c) \(h'(x)=6x+11\)

1. (a) \(h'(x)=-4x^{-2}-2x^{-3}\)
2. (b) \(g'(x)=18x-32x^{-3}\)

160 m/s

−6.67 units per metre

1. (a) \(\frac{dP}{dx}=-\tfrac12x+30\)
2. (b) 10 thousand euros per hundred items
3. (c) x = 60

a = 2, b = −5

k = 3, n = −2