How does one differentiate y=cos^-1 x (1 Viewer)

[cloud edwards]

How do you differentiate y=cos^-1x (NOTE: inverse cos), and the formula isn't given in the formula sheet.

 

[si2136]

It should be in the formula sheet. It would be

-1 / Sqrt(1 - x^2)

 

[He-Mann]

y = cos^-1x => x = cos(y) ... (*)

So, (sin(y))^2 + (cos(y))^2 = 1 means sin(y) = sqrt(1 - x^2)

Now, differentiate (*) with respect to y,

dx/dy = -sin(y) => dy/dx = -1/sin(y) = -1/sqrt(1 - x^2)

There are some missing details on plus/minus, but this is the gist of it.

 

[cloud edwards]

Sorry He-Mann, how did you get the sin(y) to equal sqrt(1 - x^2)? I'd probably sound really dumb here.

 

[kawaiipotato]

The trigonometric identity: cos^2 y + sin^2 y = 1.