Question

Find `(dy)/(dx) if y = cos^-1 (√x)`

Answer 1

Let `y = cos^-1 sqrt x`
Differentiating w.r.t.x.

`dy/dx = d/dx (cos^-1 sqrt x)` 

= `-1/sqrt( 1 - (sqrtx)^2) . d/dx sqrt x`

= `-1/sqrt( 1 - x ) xx 1/(2sqrt x)`

= `-1/[2 sqrt( x - x^2)]`