Derivative of (x - 1)ln(x)? - Applying the Product Rule

In this video, I demonstrate how to find the derivative of f(x) = (x - 1)ln(x) by noting that the function is a product of 2 smaller functions - this means the product rule can be applied to find the answer.

The product rule is defined as:

\frac{\mathrm{d} }{\mathrm{d} x}\left ( u\cdot v \right )=v\frac{\mathrm{d} u}{\mathrm{d} x}+u\frac{\mathrm{d} v}{\mathrm{d} x}

Or in shorthand form:

f' = \left (u\cdot v \right )'=vu'+uv'

So if we let...

u = x - 1
v =ln(x)

The derivatives of u and v are...

du/dx = u' = 1
dv/dx = v' = 1/x

We can then substitute these terms according into the product rule to find the derivative of (x-1)ln(x)