Question

How do you differentiate `x^2arcsinx`?

Answer 1

Use the product rule for derivatives:
`(d f(x) * g(x))/dx = (d f(x))/dx * g(x) + f(x) * (d g(x))/dx`
with
`f(x) = x^2` and
`g(x) = arcsin x`

(Note: `(d arcsin(x))/dx = 1/sqrt(1-x^2)`

`(d (x^2 arcsin(x)))/dx = 2x * arcsin(x) + x^2 * 1/(sqrt(1 - x^2))`