Question

How do you differentiate f(x) = x² ln(x) ?

Answer 1

Using the product rule,

`f^'(x) = x(2ln(x) + 1)`

Explanation:

We have that for every `f(x)` such that `f(x) = g(x)h(x)`, `f^'(x) = g^'(x)h(x) + g(x)h^'(x)`,

We know that `(x^2)^' = 2x` and that `(ln(x))^' = 1/x`, so we just evaluate it

`f^'(x) = 2x*ln(x) + x^2*1/x = 2x*ln(x) + x`

Or, putting `x` in evidence

`f^'(x) = x(2ln(x) + 1)`