`y = 3xarcsinx , (1/2, pi/4)` Find an equation of the tangent line to the graph of the function at the given point

Check that the given point belongs to the given curve:

`pi/4 = 3*1/2*arcsin(1/2)` is true, because `arcsin(1/2) = pi/6` and `3/2*pi/6 = pi/4.`

The tangent line has an equation  `(y - pi/4) = (x - 1/2)*y'(1/2),` so we need to find the derivative. The product rule is applicable here.

`y'(x) = 3(x*arcsin(x))' = 3(arcsin(x) + x/sqrt(1-x^2)),`

and at `x = 1/2` it is equal to `3*(pi/6 + (1/2)/sqrt(3/4)) = 3*(pi/6 + 1/sqrt(3)) = pi/2 + sqrt(3).`

And the equation of the tangent line is finally

`y = (pi/2 + sqrt(3))x - 1/2(pi/2 + sqrt(3)) + pi/4 =(pi/2 + sqrt(3))x - pi/4 - sqrt(3)/2 + pi/4 =(pi/2 + sqrt(3))x - sqrt(3)/2.`