How do I differentiate this

How do I differentiate y = arccos (1-2x^2) with respect to x (with a simplified answer too)?

Detailed steps would be most appreciated.

F.Y.I arccosine is inverse cosine ---- cos^-1 u

so i have this equation y = cos^-1 (1-2x^2)

to find the derivative u have to use the formula dy/dx = [-1/sqrt (1- u^2)]*(du/dx)

in this case my "u" is 1- 2x^2 ======> dy/dx = -4x

then i sub my u into the formula i have

dy/dx = [-1 / sqrt (1 - (1-2x^2)^2)]*(-4x)

= 4x / sqrt (1 - (1-2x^2)^2)

u can expand some more , as u like.

Recall that d/dx[arccos(u)] = -1/√(1 - u²) * (du/dx).

From the above rule:

y' = -1/√[1 - (1 - 2x²)²] * (-4x)

y' = 4x/√(1 - (1 - 4x² + 4x^4)

y' = 4x/√(4x² - 4x^4) = 2/√(1 - x²)

cosy = 1 - 2x^2 ;

siny = {1 - 1 + 4x^2 - 4x^4}^1/2 = 2xsqrt(1 - x^2)

- siny[dy/dx] = - 4x ;

dy/dx = 4x/siny = 4x/{2xsqrt(1 - x^2)} = 2/sqrt(1 - x^2) .