The chain rule Problem set A Answers

1. (a) \(20 \left(4 x + 1\right)^{4}\)
2. (b) \(\left(12 x^{2} - 8\right) \left(x^{3} - 2 x\right)^{3}\)

1. (a) \(\frac{4 x}{3 \sqrt[3]{x^{2} + 5}}\)
2. (b) \(\frac{6 x - 1}{2\sqrt{3 x^{2} - x}}\)

1. (a) \(5 \cos{\left(5 x \right)}\)
2. (b) \(- 3 \sin{\left(3 x - 2 \right)}\)

1. (a) \(5 e^{5 x}\)
2. (b) \(\left(2 x - 4\right) e^{x^{2} - 4 x}\)

1. (a) \(\frac{1}{x}\)
2. (b) \(\frac{2 x}{x^{2} + 4}\)

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

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

26

-2.12 °C per minute (the drink is cooling)

0.54 m per hour (rising)

\(y=\frac{3}{5}x+\frac{16}{5}\)

(1.83, 0.405)

\(y=\frac{1}{4}x+1.14\)

\(y=1.23x-1.57\)