Differentiation - Connected Rates of Change

IB AA SL: core and optional content

Core: gradient atπ/4. Optional: connected rate dy/dt.

A curve has the equation \(y = \frac{\sin x - 2}{\cos x}\).

1. Find the gradient of the curve when \(x = \frac{\pi}{4}\).

2. Given that \(x\) is increasing at a rate of \(\frac{1}{5}\) units per second, find the rate of change of \(y\) when \(x = \frac{\pi}{4}\).