Sketch the following functions along with their gradient functions on the same set of axes.

- \(f(x) = \ln (x)\)
- \(g(x) = \ln (-x)\)

What are the domains of \(f(x)\) and \(g(x)\)?

Using your sketch to help you, write down the derivatives of \(f(x)\) and \(g(x)\).

What do you notice about the derivatives \(f'(x)\) and \(g'(x)\)?

Use the applet to check your sketches of \(f(x)\), \(g(x)\) and their gradient functions.