Given $y = e^{kx}$, where $k$ is a constant, find \(rac{dy}{dx}\) - AQA - A-Level Maths Pure - Question 2 - 2019 - Paper 1

To differentiate the function (y = e^{kx}) with respect to (x), we use the chain rule. The derivative of (e^{u}) is (e^{u} \cdot \frac{du}{dx}), where (u = kx). Hence:

$\frac{dy}{dx} = e^{kx} \cdot \frac{d(kx)}{dx}$

Since (\frac{d(kx)}{dx} = k), we can substitute this back:

$\frac{dy}{dx} = k e^{kx}$

Thus, the correct answer to circle is (\frac{dy}{dx} = ke^{kx}).