If f(x) = 8x arcsin x, find f'(x).
I know that we have to apply the product rule, but something isn't adding up (no pun intended).
f'(x) = 8 (arcsin x) + 8x * 1 / (1+x^2)^2
f'(x) = 8 arcsin x + 8x / (1+8x^2)^1/2
What went wrong?
We know the derivative of arcsin (x)=1/sqrt(1-x^2).
For the product rule, we want the FIRST times the derivative of the second PLUS the SECOND times the derivative of the first.
Here, the first is 8x and the second is arcsin (x).
I get f'(x)=(8x/sqrt(1-x^2))+8 arcsin (x)