Differentiating powers of x Problem set B Answers

1. (a) \(g'(x)=7x^6\)
2. (b) \(z'(t)=-8t^{-9}\)
3. (c) \(\frac{dp}{dq}=-7q^{-8}\)

1. (a) \(\frac{dy}{dx}=30x^4\)
2. (b) \(g'(u)=-14u^6\)
3. (c) \(\frac{dy}{dx}=0\)
4. (d) \(\frac{dy}{dx}=3\)

1. (a) \(\frac{dy}{dx}=-14x^{-3}\)
2. (b) \(\frac{dy}{dt}=36t^{-5}\)
3. (c) \(f'(x)=\tfrac52x^{-2}\)
4. (d) \(\frac{dy}{dx}=-x^{-6}\)

1. (a) \(\frac{dy}{dx}=15x^2-16x+1\)
2. (b) \(\frac{dy}{dx}=3x^3-2x^4\)
3. (c) \(f'(x)=-4x+x^2\)
4. (d) \(\frac{dy}{dx}=3x^2-2-6x^{-2}\)

1. (a) \(f'(x)=20x^3-6x^2\)
2. (b) \(g'(x)=2x-2\)
3. (c) \(h'(x)=4x+7\)

1. (a) \(h'(x)=-6x^{-2}-2x^{-3}\)
2. (b) \(g'(x)=8x-50x^{-3}\)

324 thousand cells per hour

−13.3 newtons per thousand km

1. (a) \(\frac{dh}{dt}=-\tfrac32t+18\)
2. (b) 12 metres per second
3. (c) t = 12

p = 4, q = −7

k = 5, n = −4