Given that $y = ext{ln}(5x)$ find \frac{dy}{dx} - AQA - A-Level Maths Mechanics - Question 2 - 2021 - Paper 1

To differentiate the function, we apply the properties of logarithms. We have:

$y = ext{ln}(5x) = ext{ln}(5) + ext{ln}(x)$

Differentiating with respect to $x$, we use the known derivative of the natural logarithm:

$\frac{dy}{dx} = \frac{d}{dx}( ext{ln}(5) + ext{ln}(x))$

Since the derivative of a constant (here, ln(5)) is 0, we get:

$\frac{dy}{dx} = 0 + \frac{1}{x} = \frac{1}{x}$