How do you differentiate $x^2arcsinx$ ?

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Answer 1 · 2015-02-19T21:03:15

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

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

How do you differentiate x^2arcsinxx^2arcsinx?