Maths: Does it make a difference if you are differentiating....?

Question

1) inverse sin 3x
or
2) inverse sin (3x)

For number (1) without brackets around the answer is apparantely from the markscheme 3/(Squareroot(1-9x^2))
For number (2) with the brackets around 3x the answer is apparantely -24/(squareroot(1-9x^2)

I got the first answer for both of them. I'm assuming the mark scheme is right? Please help!

Answer 1

It sounds like in both of them you are looking at the number whose sin is 3x. In that case, they're the same function. (And the possibility of safely adding a constant multiple of 2 pi doesn't change the derivative any.)

Anyhow, arcsin is an increasing function when x is a small positive number, so the derivative shouldn't be a function that is negative in that range.

Answer 2

no way you can have -24/(squareroot(1-9x^2)

they were the same answer 3/(Squareroot(1-9x^2))

because they are the same question.