Question

How do you use the product rule to find the derivative of `y=x*ln(x)` ?

Answer 1

`=>y' = ln(x) + 1`

Explanation:

`y = x * ln(x)`

The product rule states that for a function `f(x) = g(x)h(x)`, the derivative is:

`f'(x) = g'(x)h(x) + g(x)h'(x)`

In our equation, we have:

• `g(x) = x`
• `h(x) = ln(x)`

We compute the derivatives:

• `g'(x) = 1`
• `h'(x) = 1/x`

We use the product rule:

`f'(x) = g'(x)h(x) + g(x)h'(x)`

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

`=>f'(x) = ln(x) + 1`