Question

What is the second derivative of #f(x) = x^2ln x #?

Answer 1

`3+ 2lnx`

Explanation:

Let's get the first derivative f'(x) first by applying the product rule:
`f(x) = x^2lnx`
`f'(x) = x^2(1/x) + (lnx)(2x)`
`f'(x) = x + 2xlnx`

Get the second derivative f''(x) by differentiating the first derivative:
Differentiate term by term. Apply product rule on the second term
`f'(x) = x + 2xlnx`
`f''(x) = 1 + 2x(1/x) + (lnx)(2)`
`f''(x) = 1 + 2 + 2lnx`
`f''(x) = 3+ 2lnx`