Week 4 Assignment (70 marks)
1. Calculate the line tangent to 𝑦 = sin(4𝑦𝑥) at 𝑥 = 1. [10 marks]
2. Find the derivative of ln(𝑦 + 𝑥) = 𝑥. [10 marks]
3. Calculate the slope of the line tangent to csc(𝑦) − 𝑥 = 3𝑥 at (𝑥, 𝑦) = (1,1). [20 marks]
2
4. Calculate the 𝑑𝑑𝑥𝑦 at (𝑥, 𝑦) = (1,1) for csc(𝑦) − 𝑥 = 3𝑥𝑦. [30 marks]