The chain rule Problem set B Answers

1. (a) \(20 \left(5 x - 2\right)^{3}\)
2. (b) \(\left(10 x + 15\right) \left(x^{2} + 3 x\right)^{4}\)

1. (a) \(\frac{3 x}{2 \sqrt[4]{x^{2} + 7}}\)
2. (b) \(\frac{4 x + 5}{2\sqrt{2 x^{2} + 5 x}}\)

1. (a) \(- 4 \sin{\left(4 x \right)}\)
2. (b) \(6 \cos{\left(6 x - 1 \right)}\)

1. (a) \(- 3 e^{- 3 x}\)
2. (b) \(\left(4 x + 1\right) e^{2 x^{2} + x}\)

1. (a) \(\frac{1}{x}\)
2. (b) \(\frac{2 x}{x^{2} + 9}\)

1. (a) \(8 \sin{\left(4 x \right)} \cos{\left(4 x \right)}\)
2. (b) \(- 5 e^{\cos{\left(5 x \right)}} \sin{\left(5 x \right)}\)
3. (c) \(\frac{1}{3 x \ln{\left(2 x \right)}^{\frac{2}{3}}}\)

1. (a) \(- 5 e^{- 5 x}\)
2. (b) \(\frac{\cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}}\)
3. (c) \(- \frac{\sin{\left(\sqrt{x} \right)}}{2 \sqrt{x}}\)

67

5.89 per cent per hour (the charge is rising)

-1.68 m per minute (falling)

\(y=\frac{5}{7}x+\frac{24}{7}\)

(0.65, 0.223)

\(y=\frac{1}{5}x+0.209\)

\(y=0.822x-1.57\)